The lcm of 12 and 11 is the smallest positive integer that divides the numbers 12 and 11 without a remainder. Spelled out, it is the least common multiple of 12 and 11. Here you can find the lcm of 12 and 11, along with a total of three methods for computing it.
What is the LCM of 12 and 11
If you just want to know what is the least common multiple of 12 and 11, it is 132. Usually, this is written as
The lcm of 12 and 11 can be obtained like this:
- The multiples of 12 are … , 120, 132, 144, ….
- The multiples of 11 are …, 121, 132, 143, …
- The common multiples of 12 and 11 are n x 132, intersecting the two sets above,
- In the intersection multiples of 12 ∩ multiples of 11 the least positive element is 132.
- Therefore, the least common multiple of 12 and 11 is 132.
Taking the above into account you also know how to find all the common multiples of 12 and 11, not just the smallest. In the next section we show you how to calculate the lcm of twelve and eleven by means of two more methods.
How to find the LCM of 12 and 11
The least common multiple of 12 and 11 can be computed by using the greatest common factor aka gcf of 12 and 11. This is the easiest approach:
Alternatively, the lcm of 12 and 11 can be found using the prime factorization of 12 and 11:
- The prime factorization of 12 is: 2 x 2 x 3
- The prime factorization of 11 is: 11
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(12,12) = 132
In any case, the easiest way to compute the lcm of two numbers like 12 and 11 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 12,11. Push the button only to start over.
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Use of LCM of 12 and 11
What is the least common multiple of 12 and 11 used for? Answer: It is helpful for adding and subtracting fractions like 1/12 and 1/11. Just multiply the dividends and divisors by 11 and 12, respectively, such that the divisors have the value of 132, the lcm of 12 and 11.
Properties of LCM of 12 and 11
The most important properties of the lcm(12,11) are:
- Commutative property: lcm(12,11) = lcm(11,12)
- Associative property: lcm(12,11,n) = lcm(lcm(11,12),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 12 and 11 is 132. In common notation: lcm (12,11) = 132.
If you have been searching for lcm 12 and 11 or lcm 12 11 then you have come to the correct page, too. The same is the true if you typed lcm for 12 and 11 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including twelve / eleven by using the search form in the sidebar of this page.
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