Tiger Algebra/core — Indonesian @ Weblate: The least common multiple (LCM), sometimes called the lowest common …

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The least common multiple (LCM), sometimes called the lowest common multiple or least common divisor (LCD), is the smallest number that two or more selected numbers can divide evenly into without a remainder. For example, <math>21</math> is the LCM of <math>3</math> and <math>7</math> because it is the lowest number that they both divide evenly into. 

There are several ways to find the LCM: listing the multiples of each number, prime factorization, the cake or ladder method, the division method, or using the greatest common factor. 

The Tiger Algebra LCM calculator not only finds the LCM but also shows the individual steps involved in doing so, helping you better understand and remember the process!

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Key	English	Indonesian
FactoringPolynomialsHavingMoreThan3Terms	Factoring polynomials with four or more terms	Memfaktorkan polinomial dengan empat suku atau lebih
FactoringPolynomialsHavingMoreThan3TermsContent	A simple way to approach factoring a polynomial with four or more terms is by grouping it into sets of two. This method involves examining these sets together to see whether a particular technique could be applied to both. One technique to start with is checking whether it is possible to find the greatest common factor (GCF) between a set of two terms. If the GCF cannot be found, the polynomials could be grouped in another way and examined for another technique. There is always the possibility that the polynomial is prime and cannot be factored. <div style="white-space: normal;"> <p>Factoring polynomials with four or more terms can be more complex than factoring binomials or trinomials. However, there are strategies that can help simplify the process.</p> <h2>Step-by-Step Process</h2> <p>To factor polynomials with four or more terms, follow these steps:</p> <ol> <li>Group the terms in pairs.</li> <li>Factor each pair using common factoring techniques such as GCF, difference of squares, or trinomial factoring.</li> <li>Look for a common factor among the resulting expressions.</li> <li>Factor out the common factor.</li> <li>Express the polynomial as the product of the common factor and the remaining expressions.</li> <li>Check your work by multiplying the factors to ensure you get the original polynomial.</li> </ol> <h2>Example</h2> <p>Let's factor the polynomial <math>x^3 + 2x^2 - 3x - 6</math>:</p> <p>Step 1: Group the terms - <math>(x^3 + 2x^2) - (3x + 6)</math>.</p> <p>Step 2: Factor each pair - <math>x^2(x + 2) - 3(x + 2)</math>.</p> <p>Step 3: Look for a common factor - Both expressions share <math>(x + 2)</math> as a common factor.</p> <p>Step 4: Factor out the common factor - <math>(x + 2)(x^2 - 3)</math>.</p> <p>Step 5: The polynomial is now factored as <math>(x + 2)(x^2 - 3)</math>.</p> <p>Factoring polynomials with four or more terms requires practice and patience, but mastering this skill can greatly simplify algebraic expressions and equations.</p> </div>	Cara sederhana untuk mendekati pemfaktoran polinomial dengan empat suku atau lebih adalah dengan mengelompokkannya ke dalam dua himpunan. Metode ini dilakukan dengan memeriksa himpunan-himpunan ini untuk mengetahui apakah teknik tertentu dapat diterapkan pada keduanya. Salah satu teknik untuk memulai adalah dengan memeriksa apakah bisa menentukan faktor persekutuan terbesar (FPB) antara himpunan dua suku. Jika FPB tidak dapat ditentukan, polinomial dapat dikelompokkan dengan cara lain dan gunakan teknik lain. Selalu ada kemungkinan bahwa polinomial merupakan bilangan prima dan tidak dapat difaktorkan.
FactorTrinomials	Factor trinomials	Faktor trinomial
FactorTrinomialsContent	<div style="white-space: normal;"> <p>Factoring trinomials is an essential skill in algebra, particularly in polynomial factorization. Trinomials are algebraic expressions with three terms, and factoring involves breaking them down into the product of two or more simpler expressions.</p> <h2>Basic Concepts</h2> <p>To factor trinomials, it's crucial to understand the following concepts:</p> <ul> <li><strong>Trinomials:</strong> Algebraic expressions with three terms, typically in the form <math>ax^2 + bx + c</math>.</li> <li><strong>Factoring:</strong> The process of expressing an algebraic expression as the product of its factors.</li> <li><strong>Factorization techniques:</strong> Methods used to factor trinomials, such as trial and error, grouping, and the quadratic formula.</li> </ul> <h2>Factoring Techniques</h2> <p>There are various techniques to factor trinomials:</p> <ul> <li><strong>Trial and error:</strong> Trying different combinations of factors until finding the correct one.</li> <li><strong>Grouping:</strong> Grouping the terms of the trinomial and factoring common factors.</li> <li><strong>Quadratic formula:</strong> Applying the quadratic formula to find the roots of the trinomial.</li> </ul> <h2>Examples</h2> <p>Let's consider a few examples to illustrate the factoring of trinomials:</p> <h3>Example 1:</h3> <p>Factor <math>x^2 + 5x + 6</math></p> <p>We look for two numbers that multiply to give 6 and add to give 5. These numbers are 2 and 3. So, <math>x^2 + 5x + 6 = (x + 2)(x + 3)</math></p> <h3>Example 2:</h3> <p>Factor <math>2x^2 + 7x + 3</math></p> <p>Using the quadratic formula, we find the roots to be <math>x = -\frac{1}{2}</math> and <math>x = -3</math>. So, <math>2x^2 + 7x + 3 = 2(x + \frac{1}{2})(x + 3)</math></p> <h2>Conclusion</h2> <p>Factoring trinomials is an important skill in algebra that finds applications in various mathematical problems and real-world scenarios. Mastering the techniques of trinomial factoring enhances problem-solving abilities and deepens understanding of algebraic concepts.</p> </div>	Tiger Algebra menunjukkan langkah-langkah cara memfaktorkan trinomial berdasarkan metode yang berbeda.
FindAreaofTrianglegivenbyits3sides	Find area of triangle given by its 3 sides	Hitung luas segitiga yang diketahui 3 sisinya
FindAreaofTrianglegivenbyits3sidesContent	To find the Area of Triangle given its 3 sides, enter the sizes of the three sides seperated by commas and wrapped in parentheses. Tiger Algebra will show you the step by step solution. Sample input: <math>(3,4,5)</math> <div style="white-space: normal;"> <p>To find the area of a triangle given its three sides (also known as the side-length formula), you can use Heron's formula. Heron's formula allows you to calculate the area of a triangle using its side lengths alone.</p> <h2>Heron's Formula</h2> <p>Heron's formula states that the area <math>A</math> of a triangle with side lengths <math>a</math>, <math>b</math>, and <math>c</math> is given by:</p> <div style="margin-left: 20px;"> <math>A = \sqrt{s(s - a)(s - b)(s - c)}</math>,<br> <i>where</i> <math>s</math> is the semi-perimeter of the triangle, calculated as:<br> <math>s = \frac{a + b + c}{2}</math>. </div> <h2>Example</h2> <p>Let's find the area of a triangle with side lengths 5, 6, and 7:</p> <div style="margin-left: 20px;"> <math>a = 5, b = 6, c = 7</math><br> <math>s = \frac{5 + 6 + 7}{2} = 9</math><br> <math>A = \sqrt{9(9 - 5)(9 - 6)(9 - 7)}</math><br> <math>A = \sqrt{9(4)(3)(2)} = \sqrt{216}</math><br> <math>A \approx 14.7</math>. </div> <p>Therefore, the area of the triangle is approximately 14.7 square units.</p> <p>Heron's formula provides an efficient method for finding the area of a triangle when you know the lengths of its sides.</p> </div>	Untuk menghitung Luas Segitiga jika diketahui 3 sisinya, masukkan ukuran ketiga sisinya yang dipisahkan dengan koma dan tutup dengan tanda kurung. Tiger Algebra akan menunjukkan langkah-langkah penyelesaiannya. Contoh input: <math>(3,4,5)</math>
FindPrimeFactors	Find prime factors	Menentukan faktor prima
FindPrimeFactorsContent	<div style="white-space: normal;"> <p>Prime factorization is the process of finding the prime numbers that multiply together to give a specific number. This is often used in mathematics to simplify fractions or solve problems involving factors.</p> <h2>Step 1: Begin with the Number</h2> <p>To find the prime factors of a number, start with the number itself. Let's take an example: 72.</p> <h2>Step 2: Divide by Prime Numbers</h2> <p>Start dividing the number by the smallest prime number, 2, and continue dividing by prime numbers until you cannot divide evenly anymore.</p> <p>For example, for 72:</p> <ul> <li>72 ÷ 2 = 36</li> <li>36 ÷ 2 = 18</li> <li>18 ÷ 2 = 9</li> <li>9 ÷ 3 = 3</li> <li>3 is already a prime number.</li> </ul> <h2>Step 3: Record the Prime Factors</h2> <p>The prime factors of 72 are 2, 2, 2, 3, and 3.</p> <h2>Step 4: Check Your Work</h2> <p>Multiply all the prime factors together to ensure you get the original number: 2 * 2 * 2 * 3 * 3 = 72.</p> <p>Finding prime factors is essential for many mathematical operations, including simplifying fractions, finding greatest common divisors, and more.</p> </div>	Bilangan prima hanya dapat dibagi dengan angka satu atau dirinya sendiri. Bilangan bulat komposit (non-prima) dapat ditulis sebagai hasil dari faktor primanya. Masukkan faktor (sembarang bilangan) atau bilangan prima (sembarang bilangan) ke dalam kalkulator aljabar dan Tiger akan menentukan faktor primanya.
GCFCalculator	Greatest common factor	Faktor persekutuan terbesar
GCFCalculatorContent	The greatest common factor (GCF), sometimes also referred to as the highest common factor (HCF) or the greatest common divisor (GCD), is the largest positive integer that a set of integers can all be divided by. For example, the largest number that 12, 24, and 32 can all be divided by is 4, so their greatest common factor is 4. Similarly, the largest number that 3, 5, and 10 can all be divided by is 1, so their greatest common factor is 1. <br><br> There are two ways to find the greatest common factor: listing the factors of each number and prime factorization. <br><br> <b>Method 1: Listing the factors of each number</b><br> List all of the factors of each number and identify the largest (greatest) factor that all the numbers have in common. <br><br> 12 - 1, 2, 3, <b>4</b>, 6, 12<br> 24 - 1, 2, 3, <b>4</b>, 6, 8, 12, 24<br> 32 - 1, 2, 3, <b>4</b>, 8, 16, 32<br><br> 4 is the greatest factor the numbers have in common, so it is the greatest common factor. <br><br> <b>Method 2: Prime factorization</b><br> Use a factor tree to identify the prime factors (factors that are prime numbers) of each number. Identify the prime factors that all the numbers have in common and multiply them together to get the greatest common factor. <br> <img src="/images/gcfTree1.png" alt="Prime factorization tree"><br> The prime factors that all of the numbers have in common are 2 and 2. Multiply these together to get the greatest common factor, 4.	Faktor persekutuan terbesar (FPB), terkadang disebut juga sebagai faktor persekutuan tertinggi atau pembagi persekutuan terbesar, adalah bilangan bulat positif terbesar yang semua himpunan bilangan bulatnya dapat dibagi. Misalnya, bilangan terbesar yang dapat membagi 12, 24, dan 32 adalah 4. Jadi, faktor persekutuan terbesarnya adalah 4. Sama halnya dengan, bilangan terbesar yang dapat membagi 3, 5, dan 10 adalah 1. Jadi, faktor persekutuan terbesarnya adalah 1. <br><br> Ada dua cara untuk menentukan faktor persekutuan terbesar: menyebutkan faktor dari setiap bilangan dan faktorisasi prima. <br><br> <b>Cara 1: Menyebutkan faktor dari setiap bilangan</b><br> Sebutkan semua faktor dari setiap bilangan dan tentukan faktor terbesar (terbanyak) yang dimiliki oleh semua bilangan tersebut. <br><br> 12 - 1, 2, 3, <b>4</b>, 6, 12<br> 24 - 1, 2, 3, <b>4</b>, 6, 8, 12, 24<br> 32 - 1, 2, 3, <b>4</b>, 8, 16, 32<br><br> 4 adalah faktor persekutuan terbesar yang ditemukan di ketiga bilangan tersebut. Jadi, FPB dari ketiga bilangan tersebut adalah 4. <br><br> <b>Cara 2: Faktorisasi prima</b><br> Gunakan pohon faktor untuk mengidentifikasi faktor prima (faktor yang merupakan bilangan prima) dari setiap bilangan. Tentukan faktor prima yang dimiliki oleh semua bilangan tersebut dan kalikan faktor yang sama untuk mendapatkan faktor persekutuan terbesar. <br> <img src="/images/gcfTree1.png" alt="Prime factorization tree"><br> Faktor prima yang dimiliki semua bilangan tersebut adalah 2 dan 2. Kalikan keduanya untuk mendapatkan faktor persekutuan terbesar, yaitu 4.
GeometricSeries	Geometric series	Deret geometris
GeometricSeriesContent	In mathematics, a geometric series is a series with a constant ratio between successive terms. For example, the series <math>1,2,4,8</math> is geometric, because each successive term can be obtained by multiplying the previous term by <math>2</math>. <div style="white-space: normal;"> <p>A geometric series is the sum of the terms of a geometric sequence. It is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.</p> <h2>General Form</h2> <p>The general form of a geometric series is:</p> <div style="margin-left: 20px;"> <math>a + ar + ar^2 + ar^3 + \ldots = \sum_{n=0}^{\infty} ar^n</math>, </div> <p>where <math>a</math> is the first term and <math>r</math> is the common ratio.</p> <h2>Sum Formula</h2> <p>The sum of a finite geometric series with <math>n</math> terms is given by the formula:</p> <div style="margin-left: 20px;"> <math>S_n = a \frac{1 - r^n}{1 - r}</math>, </div> <p>where <math>S_n</math> is the sum of the first <math>n</math> terms.</p> <h2>Properties</h2> <ul> <li>If the absolute value of the common ratio <math>r</math> is less than 1, the series converges to a finite value.</li> <li>If the absolute value of <math>r</math> is greater than or equal to 1, the series diverges.</li> <li>The sum of an infinite geometric series can be found using the formula for the sum of an infinite geometric series:</li> <div style="margin-left: 20px;"> <math>S_{\infty} = \frac{a}{1 - r}</math>. </div> </ul> <h2>Applications</h2> <p>Geometric series have various applications in mathematics, physics, engineering, and finance. They are used to model growth and decay processes, calculate interest, analyze circuits, and more.</p> <p>Understanding geometric series and their properties is essential for solving problems in many fields.</p> </div>	Dalam matematika, deret geometri adalah deret bilangan yang memiliki perbandingan tetap antara suku-suku yang berurutan. Misalnya, deret <math>1,2,4,8</math> adalah deret geometri karena setiap suku yang berurutan dapat diperoleh dengan mengalikan suku-suku sebelumnya dengan <math>2</math>.
IdentifyingPerfectCubes	Identifying perfect cubes	Mengidentifikasi kubik sempurna
IdentifyingPerfectCubesContent	<div style="white-space: normal;"> <p>In general, a perfect cube is represented as <math>n^3</math>, where <math>n</math> is an integer.</p> <p>There are several techniques to identify perfect cubes:</p> <ul> <li><strong>Examine the last digit:</strong> Perfect cubes have specific patterns in their last digit. By examining the last digit of a number, you can often determine if it's a perfect cube.</li> <li><strong>Prime factorization:</strong> Another method is to perform prime factorization of the number and check if each prime factor appears in groups of three.</li> <li><strong>Use a table of cubes:</strong> Memorizing the cubes of numbers from 1 to 10 can help quickly identify perfect cubes.</li> </ul> <h2>Examples</h2> <p>Let's consider a few examples to illustrate the identification of perfect cubes:</p> <h3>Example 1:</h3> <p>Identify whether 64 is a perfect cube.</p> <p>Using the examination of the last digit method, we find that the last digit of 64 is 4. The last digits of perfect cubes cycle in a specific pattern (0, 1, 8, 7, 4, 5, 6, 3, 2, 9), and 4 is in this cycle. Hence, 64 is a perfect cube.</p> <h3>Example 2:</h3> <p>Identify whether 1000 is a perfect cube.</p> <p>By performing prime factorization, we find that <math>1000 = 2^3 \times 5^3</math>. Since both 2 and 5 appear in groups of three, 1000 is a perfect cube.</p> <h2>Conclusion</h2> <p>Identifying perfect cubes is an important skill in mathematics that finds applications in various fields. By understanding the basic concepts and techniques, one can easily recognize perfect cubes and utilize them in problem-solving.</p> </div>	Kubik (pangkat tiga) sempurna adalah kubik dari polinomial lain. Pemecah Soal Tiger Algebra menentukan kubik sempurna lalu menunjukkan langkah-langkah penyelesaiannya.
LCMCalculator	Least common multiple (LCM)	Kalkulator KPK
LCMCalculatorContent	The least common multiple (LCM), sometimes called the lowest common multiple or least common divisor (LCD), is the smallest number that two or more selected numbers can divide evenly into without a remainder. For example, <math>21</math> is the LCM of <math>3</math> and <math>7</math> because it is the lowest number that they both divide evenly into.<br><br> There are several ways to find the LCM: listing the multiples of each number, prime factorization, the cake or ladder method, the division method, or using the greatest common factor.<br><br> The Tiger Algebra LCM calculator not only finds the LCM but also shows the individual steps involved in doing so, helping you better understand and remember the process!	Kelipatan persekutuan terkecil (KPK), terkadang disebut kelipatan persekutuan terkecil atau pembagi persekutuan terkecil, adalah bilangan terkecil yang dapat dibagi tanpa sisa oleh dua bilangan tertentu atau lebih. Misalnya, <math>21</math> adalah KPK dari <math>3</math> dan <math>7</math> karena merupakan angka terkecil yang dapat dibagi oleh keduanya tanpa sisa.<br><br> Ada beberapa cara untuk menentukan KPK: menyebutkan kelipatan setiap bilangan, faktorisasi prima, metode kue atau tangga, metode pembagian, atau menggunakan faktor persekutuan terbesar.<br><br> Kalkulator KPK Tiger Algebra tidak hanya menentukan KPK, tetapi juga menunjukkan setiap langkah yang digunakan sehingga Anda dapat lebih memahami dan mengingat prosesnya!
LinearEquationswithOneUnknown	Linear equations with one unknown	Persamaan linear dengan satu variabel tidak diketahui
LinearEquationswithOneUnknownContent	The main application of linear equations is solving problems in which an unknown variable, usually (but not always) x, is dependent on a known constant.<br>We solve linear equations by isolating the unknown variable on one side of the equation and simplifying the rest of the equation. When simplifying, <b>anything that is done to one side of the equation must also be done to the other</b>.<br><br>An equation of:<br> <math>ax+b=0</math><br> in which <math>a</math> and <math>b</math> are the constants and <math>x</math> is the unknown variable, is a typical linear equation with one unknown. To solve for <math>x</math> in this example, we would first isolate it by subtracting <math>b</math> from both sides of the equation. We would then divide both sides of the equation by <math>a</math>, resulting in an answer of:<br><math>x = -b/a</math>	Aplikasi utama persamaan linear adalah memecahkan soal masalah variabel yang tidak diketahui, biasanya (tetapi tidak selalu) x, bergantung pada konstanta yang diketahui.<br>Kami memecahkan soal persamaan linear dengan mengisolasi variabel yang tidak diketahui pada satu sisi persamaan dan menyederhanakan sisa persamaan. Saat menyederhanakan, <b></b>apa pun yang dilakukan pada satu sisi persamaan juga harus dilakukan pada sisi lainnya.<br><br>Persamaan dari:<br> <math>ax+b=0</math><br> dengan <math>a</math> dan <math>b</math> merupakan konstanta dan <math>x</math> adalah variabel yang tidak diketahui, merupakan persamaan linear khusus dengan satu variabel yang tidak diketahui. Untuk memecahkan soal <math>x</math> dalam contoh ini, pertama-tama kita akan memisahkannya dengan mengurangkan <math>b</math> dari kedua sisi persamaan. Selanjutnya, kita akan membagi kedua sisi persamaan dengan <math>a</math> sehingga diperoleh hasil:<br><math>x = -b/a</math>
LinearEquationswithThreeUnknowns	Linear equations with three unknowns	Persamaan linear dengan tiga variabel tidak diketahui
LinearEquationswithThreeUnknownsContent	A linear system of three equations with three variables is any system that can be written in the form.<br><br> where the constants (a,b,c,d,e,f,g,h and i) can be zero as long as each equation has at least one variable (x,y or z) in it. <br><br> In addition, for the system to be called linear, the variables can only to the first power, are only in the numerator and there are no products of variables in any of the equations. <br><br> A solution to a system of equations are values of x, y and z such that, when substituted into the equations, satisfies both equations at the same time. <br><br> Separate your equations with a semi-colon ";"" when feeding them to the Tiger.	Sistem persamaan linear tiga variabel adalah sistem apa pun yang dapat ditulis dalam bentuk tersebut.
LinearEquationswithTwoUnknowns	Linear equations with two unknowns	Persamaan linear dengan dua variabel tidak diketahui
LinearEquationswithTwoUnknownsContent	A linear system of two equations with two variables is any system that can be written in the form. <br><br> <math>ax+by=p</math> <br> <math>cx+dy=q</math> <br><br> where the constants (a,b,c and d) can be zero as long as each equation has at least one variable (x or y) in it. In addition, for the system to be called linear, the variables can only to the first power, are only in the numerator and there are no products of variables in any of the equations. <br><br> A solution to a system of equations is a value of x and a value of y that, when substituted into the equations, satisfies both equations at the same time. <br><br> Separate you equations with a semi-colon ";" when feeding them to the Tiger	Sistem persamaan linear dua variabel adalah sistem apa pun yang dapat ditulis dalam bentuk tersebut.<br><br> <math>ax+by=p</math> <br> <math>cx+dy=q</math> <br><br> dengan konstanta (a,b,c, dan d) dapat bernilai nol selagi persamaan memiliki setidaknya satu variabel (x atau y) di dalamnya. Selain itu, untuk sistem yang disebut linear, dengan variabel hanya bisa pangkat pertama, hanya dalam pembilang dan tidak ada hasil variabel dalam persamaan apa pun. <br><br> Penyelesaian dari suatu sistem persamaan adalah nilai x dan nilai y yang, jika disubstitusikan ke dalam persamaan, akan memenuhi kedua persamaan secara bersamaan. <br><br> Pisahkan persamaan dengan titik koma ";" saat memasukannya ke Tiger
LinearEquationsWithFourUnknowns	Linear equations with four unknowns	Persamaan linear dengan empat variabel tidak diketahui
LinearEquationsWithFourUnknownsContent	A group of four linear equations with four unknown factors forms a system of equations. To solve this system means finding the value of the unknown factors in a manner that verifies all of the equations in the system. The overall concept behind solving a system of equations is combining the equations in such a way that the number of variables is reduced. This can be done by substitution or elimination (also called row reduction), but also by graphing or using matrices. <div style="white-space: normal;"> <p>Linear equations with four unknowns are equations where each term is either a constant or a product of a constant and one of the four variables raised to the power of 1. The general form of such equations is:</p> <div style="margin-left: 20px;"> <math>a_1x + b_1y + c_1z + d_1w = k_1</math><br> <math>a_2x + b_2y + c_2z + d_2w = k_2</math><br> <math>a_3x + b_3y + c_3z + d_3w = k_3</math><br> <math>a_4x + b_4y + c_4z + d_4w = k_4</math>, </div> <p>where <math>x</math>, <math>y</math>, <math>z</math>, and <math>w</math> are the unknown variables, and <math>a_i, b_i, c_i, d_i</math> (for <math>i = 1, 2, 3, 4</math>) and <math>k_i</math> are constants.</p> <h2>Solving Methods</h2> <p>There are several methods to solve systems of linear equations with four unknowns, including:</p> <ul> <li><strong>Matrix Methods:</strong> Such as Gauss elimination or Cramer's rule.</li> <li><strong>Substitution:</strong> Solve one equation for one variable and substitute it into the other equations.</li> <li><strong>Elimination:</strong> Add or subtract equations to eliminate one variable at a time.</li> <li><strong>Row Reduction:</strong> Use row reduction techniques to transform the augmented matrix to row-echelon or reduced row-echelon form.</li> </ul> <h2>Example</h2> <p>Let's consider the following system of linear equations with four unknowns:</p> <div style="margin-left: 20px;"> <math>3x + 2y - z + 4w = 7</math><br> <math>2x - y + 3z - 2w = -5</math><br> <math>x + 2y + 2z - 3w = 8</math><br> <math>4x - y - z + 2w = -3</math>.<br> </div> <p>We can solve this system using any of the methods mentioned above to find the values of <math>x</math>, <math>y</math>, <math>z</math>, and <math>w</math>.</p> <p>Understanding how to solve systems of linear equations with four unknowns is essential for various applications in mathematics, physics, engineering, and other fields.</p> </div>	Sekelompok empat persamaan linarr dengan empat faktor yang tidak diketahui akan membentuk suatu sistem persamaan. Mememecahkan soal sistem ini berarti menentukan nilai faktor yang tidak diketahui dengan cara menguji semua persamaan dalam sistem. Konsep keseluruhan dari pemecahan soal sistem persamaan adalah menggabungkan persamaan-persamaan sedemikian rupa sehingga jumlah variabel berkurang. Pemecahan soal ini tidak hanya dapat dilakukan dengan metode substitusi atau eliminasi (juga disebut penyederhanaan baris), tetapi juga dapat dengan menggambarkan grafik atau menggunakan matriks.
OtherFactorizations	Other factorizations	Faktorisasi lainnya
OtherFactorizationsContent	<div style="white-space: normal;"> <p>Factorization involves breaking down a number or algebraic expression into its constituent factors. Besides the common factorization techniques like prime factorization and polynomial factorization, there are other specialized methods used in specific contexts.</p> <h2>Specialized Techniques</h2> <ul> <li><strong>Difference of squares:</strong> Factoring expressions of the form \(a^2 - b^2\).</li> <li><strong>Sum or difference of cubes:</strong> Factoring expressions of the form \(a^3 + b^3\) or \(a^3 - b^3\).</li> <li><strong>Quadratic trinomials:</strong> Factoring quadratic expressions of the form \(ax^2 + bx + c\).</li> </ul> <h2>Applications</h2> <p>These specialized factorization techniques are commonly used in algebraic manipulations, simplifications, and solving equations.</p> </div>	<div style="white-space: normal;"> <p>La factorización implica descomponer un número o expresión algebraica en sus factores constituyentes. Además de las técnicas de factorización comunes como la factorización prima y la factorización polinomial, hay otros métodos especializados utilizados en contextos específicos.</p> <h2>Técnicas Especializadas</h2> <ul> <li><strong>Diferencia de cuadrados:</strong> Factorización de expresiones de la forma \(a^2 - b^2\).</li> <li><strong>Suma o diferencia de cubos:</strong> Factorizando expresiones de la forma \(a^3 + b^3\) o \(a^3 - b^3\).</li> <li><strong>Trinomios cuadráticos:</strong> Factorización de expresiones cuadráticas de la forma \(ax^2 + bx + c\).</li> </ul> <h2>Aplicaciones</h2> <p>Estas técnicas de factorización especializadas se utilizan comúnmente en manipulaciones algebraicas, simplificaciones y resolución de ecuaciones.</p> </div>
SolvingLinearEquationsBySubstitution	Solving linear equations by substitution	Memecahkan soal persamaan linear dengan metode substitusi
SolvingLinearEquationsBySubstitutionContent	Substitution is one of the methods for solving linear equations. It is a good choice if there is a variable with a coefficient of 1. This method involves solving one of the equations for a variable and then substituting that expression into another equation to solve for another variable. This will produce a single equation with one variable, which can then be solved algebraically. <div style="white-space: normal;"> <p>Solving linear equations by substitution is a method used to find the values of variables in an equation system. This method involves solving one of the equations for one variable and then substituting that expression into the other equations.</p> <h2>Basic Steps</h2> <p>The basic steps for solving linear equations by substitution are as follows:</p> <ol> <li><p>Choose one of the equations and solve it for one variable in terms of the other variables.</p></li> <li><p>Substitute the expression found in step 1 into the other equations.</p></li> <li><p>Solve the resulting equations for the remaining variables.</p></li> <li><p>Check the solutions obtained by substituting them back into the original equations to verify their correctness.</p></li> </ol> <h2>Example</h2> <p>Let's solve the following system of linear equations by substitution:</p> <div style="margin-left: 20px;"> <math>2x + y = 8</math><br> <math>x - 3y = -5</math>.<br> </div> <p>From the first equation, we can solve for <math>y</math>:</p> <div style="margin-left: 20px;"> <math>y = 8 - 2x</math>.<br> </div> <p>Now, we substitute this expression for <math>y</math> into the second equation:</p> <div style="margin-left: 20px;"> <math>x - 3(8 - 2x) = -5</math>.<br> </div> <p>Solving this equation gives us the value of <math>x</math>. Once we have the value of <math>x</math>, we can substitute it back into the expression we found for <math>y</math> to find the value of <math>y</math>.</p> <p>Solving linear equations by substitution is a useful technique for finding solutions to systems of equations when the equations are linear.</p> </div>	Substitusi merupakan salah satu metode untuk memecahkan soal persamaan linear. Metode ini adalah pilihan yang baik jika ada variabel dengan 1 koefisien. Metode ini dilakukan dengan terlebih dahulu memecahkan salah satu soal persamaan variabel lalu mensubstitusikan ekspresi itu ke persamaan lain untuk memecahkan soal variabel lain. Metode ini akan menghasilkan satu persamaan dengan satu variabel yang kemudian dapat dipecahkan dengan aljabar.
LinearInequalities	Linear inequalities	Pertidaksamaan linear
MultiplyingExponents	Multiplying exponents	Mengalikan eksponen
MultiplyingExponentsContent	Exponents are a shorter way of noting repeated multiplication of the same thing by itself. <br> For example <math>777*7=7^4</math> <br> The 'exponent', 4 in the above example, tells us how many times the value is being multiplied. The value being multiplied, 7 in our example, is called the 'base'. The Tiger Algebra multiplies exponents, showing you the step by step solution. <br> For example, you can enter	Eksponen adalah cara yang lebih singkat untuk mencatat perkalian berulang dari suatu bilangan dengan bilangan itu sendiri. <br> Misalnya <math>777*7=7^4</math> <br> 'Eksponen', 4 dalam contoh di atas, memberi tahu kita berapa kali nilai dikalikan. Nilai yang dikalikan, 7 dalam contoh kita, disebut 'bilangan pokok'. Tiger Algebra mengalikan eksponen dengan menunjukkan langkah-langkah penyelesaiannya. <br> Misalnya, Anda dapat memasukkan

Key	English	Indonesian
IntegerToRomanNumeralStep1Title1	Identify integer	Normalkan dan baca bilangan bulat
IntegerToRomanNumeralStep2TextUnit1	Split the number into place values: <math>{placeValues}</math>, then map each part to Roman symbols: <math>{romanPieces}</math>.	<math>{placeValues}</math>, <math>{romanPieces}</math>.
IntegerToRomanNumeralStep2Title1	Decompose place values	Uraikan menurut nilai tempat
IntegerToRomanNumeralStep3TextUnit1	Combine the mapped symbols to get the canonical Roman numeral: <math>{integerValue}</math> → <math>{romanResult}</math>.	<math>{integerValue}->{romanResult}</math>.
IntegerToRomanNumeralStep3Title1	Build Roman numeral	Gabungkan simbol Romawi
JoinBenefit1	Live Help	Live Help
JoinBenefit2	Earn rewards and prizes	Dapatkan bonus dan hadiah
JoinBenefit3	Customize everything	Sesuaikan semuanya
JoinCommunityHeadline	Join a community with 26,970,008 solved equations	Join a community with 26,970,008 solved equations
KeyboardInputMode	Keyboard	Keyboard
LatestRelatedDrillsSolved	Latest Related Drills Solved	Latihan Terkait Terbaru Dipecahkan
LatestSolved	Latest Solved	Terakhir Dipecahkan
LatestTopics	Topics	Topik
LatestVideoSectionTitle	Latest Videos	Video Terbaru
LCMCalculator	Least common multiple (LCM)	Kalkulator KPK
LCMCalculatorContent	The least common multiple (LCM), sometimes called the lowest common multiple or least common divisor (LCD), is the smallest number that two or more selected numbers can divide evenly into without a remainder. For example, <math>21</math> is the LCM of <math>3</math> and <math>7</math> because it is the lowest number that they both divide evenly into.<br><br> There are several ways to find the LCM: listing the multiples of each number, prime factorization, the cake or ladder method, the division method, or using the greatest common factor.<br><br> The Tiger Algebra LCM calculator not only finds the LCM but also shows the individual steps involved in doing so, helping you better understand and remember the process!	Kelipatan persekutuan terkecil (KPK), terkadang disebut kelipatan persekutuan terkecil atau pembagi persekutuan terkecil, adalah bilangan terkecil yang dapat dibagi tanpa sisa oleh dua bilangan tertentu atau lebih. Misalnya, <math>21</math> adalah KPK dari <math>3</math> dan <math>7</math> karena merupakan angka terkecil yang dapat dibagi oleh keduanya tanpa sisa.<br><br> Ada beberapa cara untuk menentukan KPK: menyebutkan kelipatan setiap bilangan, faktorisasi prima, metode kue atau tangga, metode pembagian, atau menggunakan faktor persekutuan terbesar.<br><br> Kalkulator KPK Tiger Algebra tidak hanya menentukan KPK, tetapi juga menunjukkan setiap langkah yang digunakan sehingga Anda dapat lebih memahami dan mengingat prosesnya!
LCMCalculatorFormattingGuide	<p>The least common multiple is the smallest number that is divisible by all other numbers in a sequence.</p> <p>For example, if you have a sequence 1, 2, 3, the Least Common Multiple is 6.</p> <p>lcm(1, 2, 3) = 6</p> <br> <h4>Common issues:</h4> <p>Don’t forget to write “lcm,” “least common multiple” or “LCM.”</p> <br> <h3>Examples</h3> <ul> <li><a href=/en/solution/least-common-multiple/lcm%20(24,20,36)/">lcm(24, 20, 36)</a></li> <li><a href="/en/solution/least-common-multiple/LCM%20of%2040%2048%2035/">LCM of 40 48 35</a></li> <li><a href="/en/solution/least-common-multiple/14,22,66LCM/">14,22,66LCM</a></li> <li><a href="/en/solution/least-common-multiple/least%20common%20multiple%201,2,3/">least common multiple 1,2,3</a></li> <li><a href="/en/solution/least-common-multiple/Lcm(21,35,20)/">Lcm(21,35,20)</a></li> </ul>	<p>Il minimo comune multiplo è il più piccolo numero che è divisibile per tutti gli altri numeri in una sequenza.</p> <p>Ad esempio, se hai una sequenza 1, 2, 3, il Minimo Comune Multiplo è 6.</p> <p>lcm(1, 2, 3) = 6</p> <br> <h4>Problemi comuni:</h4> <p>Non dimenticare di scrivere “lcm,” “minimo comune multiplo” o “LCM.”</p> <br> <h3>Esempi</h3> <ul> <li><a href=/en/solution/least-common-multiple/lcm%20(24,20,36)/">lcm(24, 20, 36)</a></li> <li><a href="/en/solution/least-common-multiple/LCM%20of%2040%2048%2035/">LCM di 40 48 35</a></li> <li><a href="/en/solution/least-common-multiple/14,22,66LCM/">14,22,66LCM</a></li> <li><a href="/en/solution/least-common-multiple/least%20common%20multiple%201,2,3/">minimo comune multiplo 1,2,3</a></li> <li><a href="/en/solution/least-common-multiple/Lcm(21,35,20)/">Lcm(21,35,20)</a></li> </ul>
LearnMoreWithTiger	Learn more with Tiger	Pelajari lebih lanjut dengan Tiger
LeastCommonMultipleSolver	Least common multiple (LCM) by prime factorization	Kelipatan persekutuan terkecil (KPK) dengan faktorisasi prima
LeastCommonMultipleSolver.plugin	the least common multiple (LCM) by prime factorization	kelipatan persekutuan terkecil (KPK) dengan faktorisasi prima
LeastCommonMultipleSolverSolverSpokenDescription	You entered an least common multiple problem!	Anda memasukkan beberapa soal yang paling tidak umum!
LeastCommonMultipleSolverStep1SingleNumber	The LCM (Least Common Multiple) of a single number is the number itself. Therefore, the LCM is {StepFinalResult}. <br><br> To find the LCM (Least Common Multiple) of a number, we need at least two numbers to compare. Could you please provide another number?	KPK (Kelipatan Persekutuan Terkecil) dari satu bilangan adalah bilangan itu sendiri. Oleh karena itu, KPK adalah {StepFinalResult}. <br><br> Untuk menemukan KPK (Kelipatan Persekutuan Terkecil) dari sebuah bilangan, kita membutuhkan setidaknya dua bilangan untuk dibandingkan. Bisakah Anda memberikan bilangan lain?
LeastCommonMultipleSolverStep2Spoken	We continue, by counting how often each prime factor appears.	Kita lanjutkan dengan menghitung frekuensi kemunculan setiap faktor prima.
LeastCommonMultipleSolverStep2TableColLCMmax	Max. occurrence	Kejadian maksimum
LeastCommonMultipleSolverStep2TableColPrimeFactor	Prime factor	Faktor prima
LeastCommonMultipleSolverStep2TableTextUnit1	The prime {Step2AllFactorsWithOneOccurrenceList.Count: factor \| factors } {Step2AllFactorsWithOneOccurrenceList:{ListElement}\|, \| and } {Step2AllFactorsWithOneOccurrenceList.Count: occurs \| occur } one time.	Faktor prima {Step2AllFactorsWithOneOccurrenceList.Count:\|} {Step2AllFactorsWithOneOccurrenceList:{ListElement}\|, \| dan } {Step2AllFactorsWithOneOccurrenceList.Count: muncul \| muncul } satu kali.
LeastCommonMultipleSolverStep2TableTextUnit2	The prime {Step2AllFactorsWithMoreOccurrencesList.Count: factor \| factors } {Step2AllFactorsWithMoreOccurrencesList:{ListElement}\|, \| and } {Step2AllFactorsWithMoreOccurrencesList.Count: occurs \| occur } more than once.	Faktor prima {Step2AllFactorsWithMoreOccurrencesList.Count: \| } {Step2AllFactorsWithMoreOccurrencesList:{ListElement}\|, \| dan } {Step2AllFactorsWithMoreOccurrencesList.Count: muncul \| muncul } muncul lebih dari sekali.
LeastCommonMultipleSolverStep2TableTextUnit3	The prime {Step2AllFactorsWithOneOccurrenceList.Count: factor \| factors } {Step2AllFactorsWithOneOccurrenceList:{ListElement}\|, \| and } {Step2AllFactorsWithOneOccurrenceList.Count: occurs \| occur } one time, while {Step2AllFactorsWithMoreOccurrencesList:{ListElement}\|, \| and } {Step2AllFactorsWithMoreOccurrencesList.Count: occurs \| occur } more than once.	Faktor prima {Step2AllFactorsWithOneOccurrenceList.Count: \| } {Step2AllFactorsWithOneOccurrenceList:{ListElement}\|, \| dan } {Step2AllFactorsWithOneOccurrenceList.Count: muncul \| muncul } muncul satu kali, sedangkan {Step2AllFactorsWithMoreOccurrencesList:{ListElement}\|, \| dan } {Step2AllFactorsWithMoreOccurrencesList.Count: muncul \| muncul } lebih dari sekali.
LeastCommonMultipleSolverStep2TableTitle	Determine the maximum number of times each prime factor ({Step2AllUniquePrimeFactorsList:{ListElement}\|, }) occurs in the factorization of the given numbers:	Tentukan maksimum berapa kali kemunculan setiap faktor prima ({Step2AllUniquePrimeFactorsList:{ListElement}\|, }) dalam faktorisasi bilangan yang diberikan:
LeastCommonMultipleSolverStep2Title	Build a prime factors table	Buat tabel faktor prima

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Indonesian 742 characters edited Current translation Translated

Kelipatan persekutuan terkecil (KPK), terkadang disebut kelipatan persekutuan terkecil atau pembagi persekutuan terkecil, adalah bilangan terkecil yang dapat dibagi tanpa sisa oleh dua bilangan tertentu atau lebih. Misalnya, <math>21</math> adalah KPK dari <math>3</math> dan <math>7</math> karena merupakan angka terkecil yang dapat dibagi oleh keduanya tanpa sisa. 

Ada beberapa cara untuk menentukan KPK: menyebutkan kelipatan setiap bilangan, faktorisasi prima, metode kue atau tangga, metode pembagian, atau menggunakan faktor persekutuan terbesar. 

Kalkulator KPK Tiger Algebra tidak hanya menentukan KPK, tetapi juga menunjukkan setiap langkah yang digunakan sehingga Anda dapat lebih memahami dan mengingat prosesnya!

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LCMCalculatorContent

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core/TigerAlgebra.Localization/Resources/TigerSharedResource.id.resx, string 478