Home » Least Common Multiple » LCM of 40 and 96

LCM of 40 and 96

The lcm of 40 and 96 is the smallest positive integer that divides the numbers 40 and 96 without a remainder. Spelled out, it is the least common multiple of 40 and 96. Here you can find the result for 40 and 96, 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 40 and 96, but also that of three or more integers including forty and ninety-six for example. Keep reading to learn everything about the lcm (40,96) and the terms related to it.

What is the Least Common Multiple of 40 and 96?

If you just want to know what is the least common multiple of 40 and 96, it is 480. Usually, this is written as

lcm(40,96) = 480


The lcm of 40 and 96 can be obtained like this:
  • The multiples of 40 are … , 440, 480, 520, ….
  • The multiples of 96 are …, 384, 480, 576, …
  • The common multiples of 40 and 96 are n x 480, intersecting the two sets above, .
  • In the intersection multiples of 40 ∩ multiples of 96 the least positive element is 480.
  • Therefore, the least common multiple of 40 and 96 is 480.

Taking the above into account you also know how to find all the common multiples of 40 and 96, not just the smallest. In the next section we show you how to calculate the lcm of forty and ninety-six by means of two more methods.

How to find the LCM of 40 and 96

The least common multiple of 40 and 96 can be computed by using the greatest common factor aka gcf of 40 and 96. This is the easiest approach:

lcm (40,96) = = 480



Alternatively, the lcm of 40 and 96 can be found using the prime factorization of 40 and 96:
  • The prime factorization of 40 is: 2 x 2 x 2 x 5
  • The prime factorization of 96 is: 2 x 2 x 2 x 2 x 2 x 3
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(40,40) = 480

In any case, the easiest way to compute the result for two numbers like 40 and 96 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 40,962,2. 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 40 and 96

What is the least common multiple of 40 and 96 used for? Answer: It is helpful for adding and subtracting fractions like 1/40 and 1/96. Just multiply the dividends and divisors by 12 and 5, respectively, such that the divisors have the value of 480, the lcm of 40 and 96.

. .

Next, we shed a light on the mathematical properties.

Properties of LCM of 40 and 96

The most important properties of the lcm(40,96) are:

  • Commutative property: lcm(40,96) = lcm(96,40)
  • Associative property: lcm(40,96,n) = lcm(lcm(96,40),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 forty / ninety-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 40 and 96 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