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LCM of 30 and 20

The lcm of 30 and 20 is the smallest positive integer that divides the numbers 30 and 20 without a remainder. Spelled out, it is the least common multiple of 30 and 20. Here you can find the result for 30 and 20, along with a total of three methods for computing it.


60

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 30 and 20, but also that of three or more integers including thirty and twenty for example. Keep reading to learn everything about the lcm (30,20) and the terms related to it.

What is the Least Common Multiple of 30 and 20?

If you just want to know what is the least common multiple of 30 and 20, it is 60. Usually, this is written as

lcm(30,20) = 60


The lcm of 30 and 20 can be obtained like this:
  • The multiples of 30 are … , 30, 60, 90, ….
  • The multiples of 20 are …, 40, 60, 80, …
  • The common multiples of 30 and 20 are n x 60, intersecting the two sets above, .
  • In the intersection multiples of 30 ∩ multiples of 20 the least positive element is 60.
  • Therefore, the least common multiple of 30 and 20 is 60.

Taking the above into account you also know how to find all the common multiples of 30 and 20, not just the smallest. In the next section we show you how to calculate the lcm of thirty and twenty by means of two more methods.

How to find the LCM of 30 and 20

The least common multiple of 30 and 20 can be computed by using the greatest common factor aka gcf of 30 and 20. This is the easiest approach:

lcm (30,20) = = 60



Alternatively, the lcm of 30 and 20 can be found using the prime factorization of 30 and 20:
  • The prime factorization of 30 is: 2 x 3 x 5
  • The prime factorization of 20 is: 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(30,30) = 60

In any case, the easiest way to compute the result for two numbers like 30 and 20 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 30,202,2. 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 30 and 20

What is the least common multiple of 30 and 20 used for? Answer: It is helpful for adding and subtracting fractions like 1/30 and 1/20. Just multiply the dividends and divisors by 2 and 3, respectively, such that the divisors have the value of 60, the lcm of 30 and 20.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 30 and 20

The most important properties of the lcm(30,20) are:

  • Commutative property: lcm(30,20) = lcm(20,30)
  • Associative property: lcm(30,20,n) = lcm(lcm(20,30),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 thirty / twenty by using the the search form in the sidebar of this page.

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– Article written by Mark, last updated on August 8th, 2023