The lcm of 10 and 12 is the smallest positive integer that divides the numbers 10 and 12 without a remainder. Spelled out, it is the least common multiple of 10 and 12. Here you can find the lcm of 10 and 12, along with a total of three methods for computing it. Show
What is the LCM of 10 and 12If you just want to know what is the least common multiple of 10 and 12, it is 60. Usually, this is written as lcm(10,12) = 60The lcm of 10 and 12 can be obtained like this:
Taking the above into account you also know how to find all the common multiples of 10 and 12, not just the smallest. In the next section we show you how to calculate the lcm of ten and twelve by means of two more methods. How to find the LCM of 10 and 12The least common multiple of 10 and 12 can be computed by using the greatest common factor aka gcf of 10 and 12. This is the easiest approach: lcm (10,12) = = 60Alternatively, the lcm of 10 and 12 can be found using the prime factorization of 10 and 12:
In any case, the easiest way to compute the lcm of two numbers like 10 and 12 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 10,12. Push the button only to start over. Similar searched terms on our site also include:
Use of LCM of 10 and 12What is the least common multiple of 10 and 12 used for? Answer: It is helpful for adding and subtracting fractions like 1/10 and 1/12. Just multiply the dividends and divisors by 6 and 5, respectively, such that the divisors have the value of 60, the lcm of 10 and 12. . . Properties of LCM of 10 and 12The most important properties of the lcm(10,12) are:
The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it. To sum up, the lcm of 10 and 12 is 60. In common notation: lcm (10,12) = 60. If you have been searching for lcm 10 and 12 or lcm 10 12 then you have come to the correct page, too. The same is the true if you typed lcm for 10 and 12 in your favorite search engine. Note that you can find the least common multiple of many integer pairs including ten / twelve by using the search form in the sidebar of this page. Questions and comments related to the lcm of 10 and 12 are really appreciated. Use the form below or send us a mail to get in touch. Please hit the sharing buttons if our article about the least common multiple of 10 and 12 has been useful to you, and make sure to bookmark our site. Thanks for your visit.
 On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 10 and 12. Follow the steps below, and let's calculate the LCM of 10 and 12. Method 1 - Prime factorizationStep 1: Create a list of all the prime factors of the numbers 10 and 12:
The prime factors of 10 are 2 and 5. Prime factorization of 10 in exponential form is: 10 = 21x51
The prime factors of 12 are 2, 2 and 3. Prime factorization of 12 in exponential form is: 12 = 22x31 Step 2: Identify the highest power of each prime number from the above boxes:Step 3: Multiply these values together:Step 4: The result:
As seen on the calculation above, we have now obtained the LCM of 10 and 12. The Least Common Multiple of 10 and 12 is 60. Method 2 - List of MultiplesFind and list multiples of each number until the first common multiple is found. This is the lowest common multiple. Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90 Multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96 Therefore,
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 10 and 12 is 60. LCM(10,12) = 60 Least Common Multiple of 10 and 12 with GCF FormulaThe formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b). GCF(10,12) = 2 LCM(10,12) = ( 10 × 12) / 2 LCM(10,12) = 120 / 2 LCM(10,12) = 60 Least Common Multiple (LCM) of 10 and 12 with PrimesLeast common multiple can be found by multiplying the highest exponent prime factors of 10 and 12. First we will calculate the prime factors of 10 and 12. Prime Factorization of 10
Prime factors of 10 are 2, 5. Prime factorization of 10 in exponential form is: 10 = 21 × 51 Prime Factorization of 12
Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is: 12 = 22 × 31 Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 12. LCM(10,12) = 22 × 51 × 31 The first step to this method of finding the Least Common Multiple of 10 and 12 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number. Let’s take a look at the multiples for each of these numbers, 10 and 12: What are the Multiples of 10? What are the Multiples of 12? Let’s take a look at the first 10 multiples for each of these numbers, 10 and 12: First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 First 10 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 10 and 12 are 60, 120, 180. Because 60 is the smallest, it is the least common multiple. The LCM of 10 and 12 is 60. The LCM of 10 and 12 is 60. Steps to find LCM
MathStep (Works offline) Android and iPhone/ iPad Find least common multiple (LCM) of: 20 & 24 5 & 6 30 & 36 50 & 60 70 & 84 20 & 12 10 & 24 30 & 12 10 & 36 50 & 12 10 & 60 70 & 12 10 & 84 Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here. |
What is the lcm for 10 and 12
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