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.
What is the LCM of 10 and 12
If you just want to know what is the least common multiple of 10 and 12, it is 60. Usually, this is written as
The lcm of 10 and 12 can be obtained like this:
- The multiples of 10 are … , 50, 60, 70, ….
- The multiples of 12 are …, 48, 60, 72, …
- The common multiples of 10 and 12 are n x 60, intersecting the two sets above,
- In the intersection multiples of 10 ∩ multiples of 12 the least positive element is 60.
- Therefore, the least common multiple of 10 and 12 is 60.
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 12
The 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:
Alternatively, the lcm of 10 and 12 can be found using the prime factorization of 10 and 12:
- The prime factorization of 10 is: 2 x 5
- The prime factorization of 12 is: 2 x 2 x 3
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(10,10) = 60
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.
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Use of LCM of 10 and 12
What 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 12
The most important properties of the lcm(10,12) are:
- Commutative property: lcm(10,12) = lcm(12,10)
- Associative property: lcm(10,12,n) = lcm(lcm(12,10),n)
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.
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