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LCM of 76 and 72

The lcm of 76 and 72 is the smallest positive integer that divides the numbers 76 and 72 without a remainder. Spelled out, it is the least common multiple of 76 and 72. Here you can find the result for 76 and 72, along with a total of three methods for computing it.


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This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 76 and 72, but also that of three or more integers including seventy-six and seventy-two for example. Keep reading to learn everything about the lcm (76,72) and the terms related to it.

What is the Least Common Multiple of 76 and 72?

If you just want to know what is the least common multiple of 76 and 72, it is 1368. Usually, this is written as

lcm(76,72) = 1368


The lcm of 76 and 72 can be obtained like this:
  • The multiples of 76 are … , 1292, 1368, 1444, ….
  • The multiples of 72 are …, 1296, 1368, 1440, …
  • The common multiples of 76 and 72 are n x 1368, intersecting the two sets above, .
  • In the intersection multiples of 76 ∩ multiples of 72 the least positive element is 1368.
  • Therefore, the least common multiple of 76 and 72 is 1368.

Taking the above into account you also know how to find all the common multiples of 76 and 72, not just the smallest. In the next section we show you how to calculate the lcm of seventy-six and seventy-two by means of two more methods.

How to find the LCM of 76 and 72

The least common multiple of 76 and 72 can be computed by using the greatest common factor aka gcf of 76 and 72. This is the easiest approach:

lcm (76,72) = = 1368



Alternatively, the lcm of 76 and 72 can be found using the prime factorization of 76 and 72:
  • The prime factorization of 76 is: 2 x 2 x 19
  • The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(76,76) = 1368

In any case, the easiest way to compute the result for two numbers like 76 and 72 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 76,722,2. 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 76 and 72

What is the least common multiple of 76 and 72 used for? Answer: It is helpful for adding and subtracting fractions like 1/76 and 1/72. Just multiply the dividends and divisors by 18 and 19, respectively, such that the divisors have the value of 1368, the lcm of 76 and 72.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 76 and 72

The most important properties of the lcm(76,72) are:

  • Commutative property: lcm(76,72) = lcm(72,76)
  • Associative property: lcm(76,72,n) = lcm(lcm(72,76),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 seventy-six / seventy-two 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