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LCM of 96 and 15

The lcm of 96 and 15 is the smallest positive integer that divides the numbers 96 and 15 without a remainder. Spelled out, it is the least common multiple of 96 and 15. Here you can find the result for 96 and 15, along with a total of three methods for computing it.


480

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 96 and 15, but also that of three or more integers including ninety-six and fifteen for example. Keep reading to learn everything about the lcm (96,15) and the terms related to it.

What is the Least Common Multiple of 96 and 15?

If you just want to know what is the least common multiple of 96 and 15, it is 480. Usually, this is written as

lcm(96,15) = 480


The lcm of 96 and 15 can be obtained like this:
  • The multiples of 96 are … , 384, 480, 576, ….
  • The multiples of 15 are …, 465, 480, 495, …
  • The common multiples of 96 and 15 are n x 480, intersecting the two sets above, .
  • In the intersection multiples of 96 ∩ multiples of 15 the least positive element is 480.
  • Therefore, the least common multiple of 96 and 15 is 480.

Taking the above into account you also know how to find all the common multiples of 96 and 15, not just the smallest. In the next section we show you how to calculate the lcm of ninety-six and fifteen by means of two more methods.

How to find the LCM of 96 and 15

The least common multiple of 96 and 15 can be computed by using the greatest common factor aka gcf of 96 and 15. This is the easiest approach:

lcm (96,15) = = 480



Alternatively, the lcm of 96 and 15 can be found using the prime factorization of 96 and 15:
  • The prime factorization of 96 is: 2 x 2 x 2 x 2 x 2 x 3
  • The prime factorization of 15 is: 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(96,96) = 480

In any case, the easiest way to compute the result for two numbers like 96 and 15 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 96,152,2. 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 96 and 15

What is the least common multiple of 96 and 15 used for? Answer: It is helpful for adding and subtracting fractions like 1/96 and 1/15. Just multiply the dividends and divisors by 5 and 32, respectively, such that the divisors have the value of 480, the lcm of 96 and 15.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 96 and 15

The most important properties of the lcm(96,15) are:

  • Commutative property: lcm(96,15) = lcm(15,96)
  • Associative property: lcm(96,15,n) = lcm(lcm(15,96),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 ninety-six / fifteen 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