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LCM of 12 and 11

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 result for 12 and 11, along with a total of three methods for computing it.


132

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 12 and 11, but also that of three or more integers including twelve and eleven for example. Keep reading to learn everything about the lcm (12,11) and the terms related to it.

What is the Least Common Multiple 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

lcm(12,11) = 132


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:

lcm (12,11) = = 132



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 result for two numbers like 12 and 11 is by using our calculator above. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 12,112,2. Push the button only to start over.

Similar searched terms on our site also include:

In the next paragraph we explain how the mathematical concept can be employed.

Keep reading – it’s really interesting.

Use of Least Common Multiple 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.

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Next, we shed a light on the mathematical properties.

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.

Summary

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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– Article written by Mark, last updated on August 8th, 2023