Home » Least Common Multiple » LCM of 12 and 66

LCM of 12 and 66

The lcm of 12 and 66 is the smallest positive integer that divides the numbers 12 and 66 without a remainder. Spelled out, it is the least common multiple of 12 and 66. Here you can find the result for 12 and 66, 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 66, but also that of three or more integers including twelve and sixty-six for example. Keep reading to learn everything about the lcm (12,66) and the terms related to it.

What is the Least Common Multiple of 12 and 66?

If you just want to know what is the least common multiple of 12 and 66, it is 132. Usually, this is written as

lcm(12,66) = 132


The lcm of 12 and 66 can be obtained like this:
  • The multiples of 12 are … , 120, 132, 144, ….
  • The multiples of 66 are …, 66, 132, 198, …
  • The common multiples of 12 and 66 are n x 132, intersecting the two sets above, .
  • In the intersection multiples of 12 ∩ multiples of 66 the least positive element is 132.
  • Therefore, the least common multiple of 12 and 66 is 132.

Taking the above into account you also know how to find all the common multiples of 12 and 66, not just the smallest. In the next section we show you how to calculate the lcm of twelve and sixty-six by means of two more methods.

How to find the LCM of 12 and 66

The least common multiple of 12 and 66 can be computed by using the greatest common factor aka gcf of 12 and 66. This is the easiest approach:

lcm (12,66) = = 132



Alternatively, the lcm of 12 and 66 can be found using the prime factorization of 12 and 66:
  • The prime factorization of 12 is: 2 x 2 x 3
  • The prime factorization of 66 is: 2 x 3 x 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 66 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 12,662,2. 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 66

What is the least common multiple of 12 and 66 used for? Answer: It is helpful for adding and subtracting fractions like 1/12 and 1/66. Just multiply the dividends and divisors by 11 and 2, respectively, such that the divisors have the value of 132, the lcm of 12 and 66.

. .

Next, we shed a light on the mathematical properties.

Properties of LCM of 12 and 66

The most important properties of the lcm(12,66) are:

  • Commutative property: lcm(12,66) = lcm(66,12)
  • Associative property: lcm(12,66,n) = lcm(lcm(66,12),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 / sixty-six by using the search form in the sidebar of this page.

Questions and comments 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 12 and 66 has been useful to you, and make sure to bookmark our site.

If you have some time left check out the related sites and resources in the sidebar of this site.

Thanks for your visit.

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