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LCM of 68 and 60

The lcm of 68 and 60 is the smallest positive integer that divides the numbers 68 and 60 without a remainder. Spelled out, it is the least common multiple of 68 and 60. Here you can find the result for 68 and 60, along with a total of three methods for computing it.


1020

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 68 and 60, but also that of three or more integers including sixty-eight and sixty for example. Keep reading to learn everything about the lcm (68,60) and the terms related to it.

What is the Least Common Multiple of 68 and 60?

If you just want to know what is the least common multiple of 68 and 60, it is 1020. Usually, this is written as

lcm(68,60) = 1020


The lcm of 68 and 60 can be obtained like this:
  • The multiples of 68 are … , 952, 1020, 1088, ….
  • The multiples of 60 are …, 960, 1020, 1080, …
  • The common multiples of 68 and 60 are n x 1020, intersecting the two sets above, .
  • In the intersection multiples of 68 ∩ multiples of 60 the least positive element is 1020.
  • Therefore, the least common multiple of 68 and 60 is 1020.

Taking the above into account you also know how to find all the common multiples of 68 and 60, not just the smallest. In the next section we show you how to calculate the lcm of sixty-eight and sixty by means of two more methods.

How to find the LCM of 68 and 60

The least common multiple of 68 and 60 can be computed by using the greatest common factor aka gcf of 68 and 60. This is the easiest approach:

lcm (68,60) = = 1020



Alternatively, the lcm of 68 and 60 can be found using the prime factorization of 68 and 60:
  • The prime factorization of 68 is: 2 x 2 x 17
  • The prime factorization of 60 is: 2 x 2 x 3 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(68,68) = 1020

In any case, the easiest way to compute the result for two numbers like 68 and 60 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 68,602,2. 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 68 and 60

What is the least common multiple of 68 and 60 used for? Answer: It is helpful for adding and subtracting fractions like 1/68 and 1/60. Just multiply the dividends and divisors by 15 and 17, respectively, such that the divisors have the value of 1020, the lcm of 68 and 60.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 68 and 60

The most important properties of the lcm(68,60) are:

  • Commutative property: lcm(68,60) = lcm(60,68)
  • Associative property: lcm(68,60,n) = lcm(lcm(60,68),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-eight / sixty 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