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LCM of 61 and 11

The lcm of 61 and 11 is the smallest positive integer that divides the numbers 61 and 11 without a remainder. Spelled out, it is the least common multiple of 61 and 11. Here you can find the result for 61 and 11, along with a total of three methods for computing it.


671

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 61 and 11, but also that of three or more integers including sixty-one and eleven for example. Keep reading to learn everything about the lcm (61,11) and the terms related to it.

What is the Least Common Multiple of 61 and 11?

If you just want to know what is the least common multiple of 61 and 11, it is 671. Usually, this is written as

lcm(61,11) = 671


The lcm of 61 and 11 can be obtained like this:
  • The multiples of 61 are … , 610, 671, 732, ….
  • The multiples of 11 are …, 660, 671, 682, …
  • The common multiples of 61 and 11 are n x 671, intersecting the two sets above, .
  • In the intersection multiples of 61 ∩ multiples of 11 the least positive element is 671.
  • Therefore, the least common multiple of 61 and 11 is 671.

Taking the above into account you also know how to find all the common multiples of 61 and 11, not just the smallest. In the next section we show you how to calculate the lcm of sixty-one and eleven by means of two more methods.

How to find the LCM of 61 and 11

The least common multiple of 61 and 11 can be computed by using the greatest common factor aka gcf of 61 and 11. This is the easiest approach:

lcm (61,11) = = 671



Alternatively, the lcm of 61 and 11 can be found using the prime factorization of 61 and 11:
  • The prime factorization of 61 is: 61
  • 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(61,61) = 671

In any case, the easiest way to compute the result for two numbers like 61 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 61,112,2. 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 61 and 11

What is the least common multiple of 61 and 11 used for? Answer: It is helpful for adding and subtracting fractions like 1/61 and 1/11. Just multiply the dividends and divisors by 11 and 61, respectively, such that the divisors have the value of 671, the lcm of 61 and 11.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 61 and 11

The most important properties of the lcm(61,11) are:

  • Commutative property: lcm(61,11) = lcm(11,61)
  • Associative property: lcm(61,11,n) = lcm(lcm(11,61),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 sixty-one / 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