Tiger Algebra/core — Serbian @ 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	Serbian
FactoringPolynomialsHavingMoreThan3Terms	Factoring polynomials with four or more terms	Faktorizacija polinoma sa četiri ili više članova
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>	Jednostavan način za pristup faktorizaciji polinoma sa četiri ili više članova jeste grupisanje u skupove od dva člana. Ovaj metod uključuje ispitivanje ovih skupova da bi se videlo da li se neka posebna tehnika može primeniti za oba. Jedna od tehnika kojom bi trebalo započeti jeste provera da li je moguće naći najveći zajednički delilac (NZD) za dva člana u skupu. Ako nije moguće naći NZD, polinomi se mogu grupisati na drugi način i primeniti neku drugu tehniku za ispitivanje. Uvek postoji mogućnost da je polinom prost i da se ne može faktorizovati.
FactorTrinomials	Factor trinomials	Faktorizacija trinoma
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 vam pokazuje korak po korak kako da faktorizujete trinome pomoću različitih metoda.
FindAreaofTrianglegivenbyits3sides	Find area of triangle given by its 3 sides	Pronađi površinu trougla pomoću njegove 3 stranice
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>	Da biste pronašli površinu trougla pomoću njegove 3 stranice, unesite veličine sve tri stranice, razdvojeno zarezima i ubačeno u zagrade. Tiger Algebra će vam pokazati postepeno kako da dođete do rešenja. Unos uzorka: <math>(3,4,5)</math>
FindPrimeFactors	Find prime factors	Pronađi proste faktore
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>	Prost broj se može podeliti samo sa jedinicom ili samim sobom. Složeni (koji nisu prosti) celi brojevi mogu se pisati kao proizvod njihovih prostih faktora. Unesi faktore (bilo koji broj) ili proste brojeve (bilo koji broj) u algebarski kalkulator i Tiger će pronaći njihove proste faktore za tebe.
GCFCalculator	Greatest common factor	Najveći zajednički delilac
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.	Najveći zajednički delilac (NZD), koji se ponekad naziva i najviši zajednički faktor (NZF) ili najveći zajednički delilac (NZD), najveći je pozitivni celi broj sa kojim se skup celih brojeva može podeliti. Na primer, najveći broj sa kojim se svi 12, 24 i 32 mogu podeliti je 4, pa je njihov najveći zajednički delilac 4. Slično tome, najveći broj sa kojim se 3, 5 i 10 mogu podeliti je 1, pa je njihov najveći zajednički delilac 1. <br><br> Postoje dva načina za pronalaženje najvećeg zajedničkog delioca: navođenje delioca svakog broja i faktorizacija prostog broja. <br><br> <b>Metod 1: Navođenje delioca svakog broja</b><br> Navedi sve delioce svakog broja i identifikuj najveći (najviši) delilac koji je zajednički sa svim brojevima. <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 je najveći zajednički delilac koji brojevi imaju, pa je i najveći zajednički delilac. <br><br> <b>Metod 2: Faktorizacija prostog broja</b><br> Koristi stablo faktora za identifikaciju prostih faktora (faktora koji su prosti brojevi) svakog broja. Identifikuj proste faktore koji su zajednički sa svim brojevima i pomnoži ih da biste dobili najveći zajednički delilac. <br> <img src="/images/gcfTree1.png" alt="Prime factorization tree"><br> Prosti faktori koji su zajednički sa svim brojevima su 2 i 2. Pomnoži ih zajedno da dobiješ najveći zajednički delilac, 4.
GeometricSeries	Geometric series	Geometrijski red
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>	U matematici, geometrijski red predstavlja red sa konstantnom srazmerom između uzastopnih članova. Na primer, red <math>1,2,4,8</math> je geometrijski zato što se svaki uzastopni član može dobiti množenjem prethodnog člana sa <math>2</math>.
IdentifyingPerfectCubes	Identifying perfect cubes	Identifikovanje savršenih kubova
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>	Savršeni kub je kub drugog polinoma. Rešavač Tiger Algebra nalazi savršene kubove i pokazuje vam postepeno rešavanje problema.
LCMCalculator	Least common multiple (LCM)	NSZ kalkulator
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!	Najmanji zajednički sadržilac (NZS), koji se ponekad naziva i najniži zajednički sadržilac ili najmanji zajednički delilac (NZD), je najmanji broj na koji dva ili više odabranih brojeva mogu ravnomerno da se podele bez ostatka. Na primer, <math>21</math> je NZS od <math>3</math> i <math>7</math> jer je to najmanji broj na koji se oba ravnomerno dele.<br><br> Postoji nekoliko načina za pronalaženje NZS-a: navođenje sadržilaca svakog broja, faktorizacija prostog broja, metod kolača ili merdevina, metod deljenja ili korišćenje najvećeg zajedničkog delioca.<br><br> Tiger Algebra LCM kalkulator ne samo da pronalazi NZS, već i pokazuje pojedinačne korake koji su uključeni u to, pomažući vam da bolje razumete i zapamtite proces!
LinearEquationswithOneUnknown	Linear equations with one unknown	Linearne jednačine sa jednom nepoznatom
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>	Glavna primena linearnih jednačina je za rešavanje problema u kojima nepoznata promenljiva zavisi od poznate promenljive.<br>Linearne jednačine rešavamo razdvajanjem (ponekad se opisuje kao „izolovanje”) nepoznate promenljive od ostatka jednačine. Nepoznata promenljiva se obično, mada ne uvek, piše sa „x”. Kod uprošćavanja, <b>sve što uradite na jednoj strani jednačine takođe morati uraditi i na drugoj strani jednačine</b>.<br><br>Jednačina:<br> <math>ax+b=0</math><br> u kojoj su <math>a</math> i <math>b</math> konstante, a <math>x</math> je nepoznata varijabla, koja predstavlja tipičnu linearnu jednačinu sa jednom nepoznatom. Da bi se pronašlo rešenje za <math>x</math> u ovom primeru, prvo ćemo ga izolovati oduzimanjem <math>b</math> od obe strane jednačine. Zatim ćemo podeliti obe strane jednačine sa <math>a</math>, što će dovesti do odgovora:<br><math>x = -b/a</math>
LinearEquationswithThreeUnknowns	Linear equations with three unknowns	Linearne jednačine sa tri nepoznate
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.	Linearni sistem od tri jednačine sa tri promenljive predstavlja bilo koji sistem koji se može pisati u obliku.
LinearEquationswithTwoUnknowns	Linear equations with two unknowns	Linearne jednačine sa dve nepoznate
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	Linearni sistem od dve jednačine sa dve promenljive jeste bilo koji sistem koji se može pisati u obliku. <br><br> <math>ax+by=p</math> <br> <math>cx+dy=q</math> <br><br> pri čemu konstante (a, b, c i d) mogu biti nula sve dok svaka jednačina u sebi ima barem jednu promenljivu (x ili y). Pored toga, da bi se sistem mogao nazvati linearnim, promenljive mogu biti samo do prvog stepena, nalaze se samo u brojiocu i nema proizvoda promenljivih ni u jednoj od jednačina. <br><br> Rešenje sistema jednačina su vrednosti za x i y, koje kada se zamene u jednačinama zadovoljavaju obe jednačine istovremeno. <br><br> Razdvoji svoje jednačine pomoću tačke sa zarezom (;) onda kada ih postavljaš na Tiger.
LinearEquationsWithFourUnknowns	Linear equations with four unknowns	Linearne jednačine sa četiri nepoznate
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>	Grupa od četiri linearne jednačine sa četiri nepoznate čini sistem jednačina. Rešavanje ovog sistema znači pronalaženje vrednosti nepoznatih činioca tako da svaka jednačina u sistemu bude ispravna. Opšti koncept koji stoji iza rešavanja sistema jednačina predstavlja kombinovanje jednačina na takav način da se smanji broj promenljivih. To se može uraditi supstitucijom (zamenom) ili eliminacijom (poznato takođe pod nazivom redukcija redova), ali takođe i grafičkim putem ili korišćenjem matrica.
OtherFactorizations	Other factorizations	Druge faktorizacije
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>Faktorizacija podrazumeva razlaganje broja ili algebarskog izraza na njegove sastavne faktore. Pored zajedničkih tehnika faktorizacije kao što su faktorizacija primarnih brojeva i faktorizacija polinoma, postoje i druge specijalizovane metode koje se koriste u specifičnim kontekstima.</p> <h2>Specijalizovane Tehnike</h2> <ul> <li><strong>Razlika kvadrata:</strong> Faktorizacija izraza oblika \(a^2 - b^2\).</li> <li><strong>Zbir ili razlika kubova:</strong> Faktorizacija izraza oblika \(a^3 + b^3\) ili \(a^3 - b^3\).</li> <li><strong>Kvadratni trinomi:</strong> Faktorizacija kvadratnih izraza oblika \(ax^2 + bx + c\).</li> </ul> <h2>Primene</h2> <p>Ove specijalizovane tehnike faktorizacije se često koriste u algebarskim manipulacijama, pojednostavljenjima i rešavanju jednačina.</p> </div>
SolvingLinearEquationsBySubstitution	Solving linear equations by substitution	Rešavanje linearnih jednačina putem supstitucije
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>	Supstitucija (zamena) je jedan od metoda za rešavanje linearnih jednačina. Dobar je izbor onda kada postoji promenljiva sa koeficijentom 1. Ovim metodom se rešava jedna od jednačina po jednoj promenljivoj, a potom se vrši zamena tog izraza u drugoj jednačini da bi se našlo rešenje za drugu promenljivu. Na ovaj način, dobija se jedna jednačina sa jednom promenljivom, što se onda može rešiti algebarski.
LinearInequalities	Linear inequalities	Linearne nejednačine
MultiplyingExponents	Multiplying exponents	Množenje stepena
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	Stepeni su kraći način za beleženje ponavljanih množenja iste veličine sa samom sobom. <br> Na primer: <math>777*7=7^4</math> <br> „Stepen” (u gornjem primeru „4”) nam pokazuje koliko puta je neka veličina pomnožena. Veličina koja se množi (u našem primeru „7”) naziva se „osnova”. Tiger Algebra množi stepene, pokazujući vam postepeno rešavanje problema. <br> Na primer, možete da unesete

Key	English	Serbian
IntegerToRomanNumeralStep1Title1	Identify integer	Normalizuj i procitaj ceo broj
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	Rastavi po mestnim vrednostima
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	Spoji rimske simbole
JoinBenefit1	Live Help	Uživo pomoć
JoinBenefit2	Earn rewards and prizes	Zaradite priznanja i nagrade
JoinBenefit3	Customize everything	Prilagodite sve
JoinCommunityHeadline	Join a community with 26,970,008 solved equations	Pridruži se zajednici sa 26,970,008 rešenih jednačina
KeyboardInputMode	Keyboard	Tastatura
LatestRelatedDrillsSolved	Latest Related Drills Solved	Rešena najnovija srodna vežbanja
LatestSolved	Latest Solved	Poslednje rešeno
LatestTopics	Topics	Teme
LatestVideoSectionTitle	Latest Videos	Novi Klipovi
LCMCalculator	Least common multiple (LCM)	NSZ kalkulator
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!	Najmanji zajednički sadržilac (NZS), koji se ponekad naziva i najniži zajednički sadržilac ili najmanji zajednički delilac (NZD), je najmanji broj na koji dva ili više odabranih brojeva mogu ravnomerno da se podele bez ostatka. Na primer, <math>21</math> je NZS od <math>3</math> i <math>7</math> jer je to najmanji broj na koji se oba ravnomerno dele.<br><br> Postoji nekoliko načina za pronalaženje NZS-a: navođenje sadržilaca svakog broja, faktorizacija prostog broja, metod kolača ili merdevina, metod deljenja ili korišćenje najvećeg zajedničkog delioca.<br><br> Tiger Algebra LCM kalkulator ne samo da pronalazi NZS, već i pokazuje pojedinačne korake koji su uključeni u to, pomažući vam da bolje razumete i zapamtite proces!
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>Najmanji zajednički višestruki broj je najmanji broj koji je deljiv sa svim drugim brojevima u nizu.</p> <p>Na primer, ako imate niz 1, 2, 3, Najmanji Zajednički Višestruki broj je 6.</p> <p>nzv(1, 2, 3) = 6</p> <br> <h4>Uobičajeni problemi:</h4> <p>Ne zaboravite da napišete “nzv,” “najmanji zajednički višestruki broj” ili “NZV.”</p> <br> <h3>Primeri</h3> <ul> <li><a href=/en/solution/naјmanji-zajednički-višestruki-broj/nzv%20(24,20,36)/">nzv(24, 20, 36)</a></li> <li><a href="/en/solution/naјmanji-zajednički-višestruki-broj/NZV%20od%2040%2048%2035/">NZV od 40 48 35</a></li> <li><a href="/en/solution/naјmanji-zajednički-višestruki-broj/14,22,66NZV/">14,22,66NZV</a></li> <li><a href="/en/solution/naјmanji-zajednički-višestruki-broj/naјmanji-zajednički-višestruki-broj%201,2,3/">naјmanji zajednički višestruki broj 1,2,3</a></li> <li><a href="/en/solution/naјmanji-zajednički-višestruki-broj/Nzv(21,35,20)/">Nzv(21,35,20)</a></li> </ul>
LearnMoreWithTiger	Learn more with Tiger	Naučite više uz Tiger
LeastCommonMultipleSolver	Least common multiple (LCM) by prime factorization	Najmanji zajednički sadržalac (NZS) prema faktorizaciji prostog broja
LeastCommonMultipleSolver.plugin	the least common multiple (LCM) by prime factorization	najmanjem zajedničkom sadržaocu (NZS) prema faktorizaciji prostog broja
LeastCommonMultipleSolverSolverSpokenDescription	You entered an least common multiple problem!	Uneli ste problem najmanjeg zajedničkog sadržaoca!
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?	Najmanji zajednički višekratnik (NZV) jednog broja je sam broj. Dakle, NZV je {StepFinalResult}. <br><br> Da bismo pronašli NZV (Najmanji zajednički višekratnik) broja, potrebna su nam barem dva broja za upoređivanje. Da li možete da nam pružite još jedan broj?
LeastCommonMultipleSolverStep2Spoken	We continue, by counting how often each prime factor appears.	Nastavljamo, brojeći koliko puta se svaki prosti faktor pojavljuje.
LeastCommonMultipleSolverStep2TableColLCMmax	Max. occurrence	Maksimalna pojava
LeastCommonMultipleSolverStep2TableColPrimeFactor	Prime factor	Prosti faktor
LeastCommonMultipleSolverStep2TableTextUnit1	The prime {Step2AllFactorsWithOneOccurrenceList.Count: factor \| factors } {Step2AllFactorsWithOneOccurrenceList:{ListElement}\|, \| and } {Step2AllFactorsWithOneOccurrenceList.Count: occurs \| occur } one time.	Prosti faktor {Step2AllFactorsWithOneOccurrenceList.Count: faktor \| faktori } {Step2AllFactorsWithOneOccurrenceList:{ListElement}\|, \| i } {Step2AllFactorsWithOneOccurrenceList.Count: se pojavljuje \| se pojavljuju } jednom.
LeastCommonMultipleSolverStep2TableTextUnit2	The prime {Step2AllFactorsWithMoreOccurrencesList.Count: factor \| factors } {Step2AllFactorsWithMoreOccurrencesList:{ListElement}\|, \| and } {Step2AllFactorsWithMoreOccurrencesList.Count: occurs \| occur } more than once.	Prosti faktor {Step2AllFactorsWithMoreOccurrencesList.Count: faktor \| faktori } {Step2AllFactorsWithMoreOccurrencesList:{ListElement}\|, \| i } {Step2AllFactorsWithMoreOccurrencesList.Count: se pojavljuje \| se pojavljuju } više od jednom.
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.	Prosti faktor {Step2AllFactorsWithOneOccurrenceList.Count: faktor \| faktori } {Step2AllFactorsWithOneOccurrenceList:{ListElement}\|, \| i } {Step2AllFactorsWithOneOccurrenceList.Count: se pojavljuje \| se pojavljuju } jednom, dok se {Step2AllFactorsWithMoreOccurrencesList:{ListElement}\|, \| i } {Step2AllFactorsWithMoreOccurrencesList.Count: pojavljuje \| pojavljuju } više od jednom.
LeastCommonMultipleSolverStep2TableTitle	Determine the maximum number of times each prime factor ({Step2AllUniquePrimeFactorsList:{ListElement}\|, }) occurs in the factorization of the given numbers:	Odredi maksimalan broj pojava svakog prostog faktora ({Step2AllUniquePrimeFactorsList:{ListElement}\|, }) u faktorizaciji datih brojeva:
LeastCommonMultipleSolverStep2Title	Build a prime factors table	Napravi tabelu prostih faktora

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Serbian 734 characters edited Current translation Translated

Najmanji zajednički sadržilac (NZS), koji se ponekad naziva i najniži zajednički sadržilac ili najmanji zajednički delilac (NZD), je najmanji broj na koji dva ili više odabranih brojeva mogu ravnomerno da se podele bez ostatka. Na primer, <math>21</math> je NZS od <math>3</math> i <math>7</math> jer je to najmanji broj na koji se oba ravnomerno dele. 

Postoji nekoliko načina za pronalaženje NZS-a: navođenje sadržilaca svakog broja, faktorizacija prostog broja, metod kolača ili merdevina, metod deljenja ili korišćenje najvećeg zajedničkog delioca. 

Tiger Algebra LCM kalkulator ne samo da pronalazi NZS, već i pokazuje pojedinačne korake koji su uključeni u to, pomažući vam da bolje razumete i zapamtite proces!

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LCMCalculatorContent

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