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LCM of 5 and 40

The lcm of 5 and 40 is the smallest positive integer that divides the numbers 5 and 40 without a remainder. Spelled out, it is the least common multiple of 5 and 40. Here you can find the result for 5 and 40, along with a total of three methods for computing it.


40

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 5 and 40, but also that of three or more integers including five and forty for example. Keep reading to learn everything about the lcm (5,40) and the terms related to it.

What is the Least Common Multiple of 5 and 40?

If you just want to know what is the least common multiple of 5 and 40, it is 40. Usually, this is written as

lcm(5,40) = 40


The lcm of 5 and 40 can be obtained like this:
  • The multiples of 5 are … , 35, 40, 45, ….
  • The multiples of 40 are …, 0, 40, 80, …
  • The common multiples of 5 and 40 are n x 40, intersecting the two sets above, .
  • In the intersection multiples of 5 ∩ multiples of 40 the least positive element is 40.
  • Therefore, the least common multiple of 5 and 40 is 40.

Taking the above into account you also know how to find all the common multiples of 5 and 40, not just the smallest. In the next section we show you how to calculate the lcm of five and forty by means of two more methods.

How to find the LCM of 5 and 40

The least common multiple of 5 and 40 can be computed by using the greatest common factor aka gcf of 5 and 40. This is the easiest approach:

lcm (5,40) = = 40



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

In any case, the easiest way to compute the result for two numbers like 5 and 40 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 5,402,2. 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 5 and 40

What is the least common multiple of 5 and 40 used for? Answer: It is helpful for adding and subtracting fractions like 1/5 and 1/40. Just multiply the dividends and divisors by 8 and 1, respectively, such that the divisors have the value of 40, the lcm of 5 and 40.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 5 and 40

The most important properties of the lcm(5,40) are:

  • Commutative property: lcm(5,40) = lcm(40,5)
  • Associative property: lcm(5,40,n) = lcm(lcm(40,5),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 five / forty 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