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 lcm of 30 and 20, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the lcm 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 LCM 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, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • 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) = $\frac{30 \times 20}{gcf(30,20)} = \frac{600}{10}$ = 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 lcm of two numbers like 30 and 20 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 30,20. Push the button only to start over.

The lcm is...
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Use of LCM 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.

$\frac{1}{30} + \frac{1}{20} = \frac{2}{60} + \frac{3}{60} = \frac{5}{60}$. $\hspace{30px}\frac{1}{30} – \frac{1}{20} = \frac{2}{60} – \frac{3}{60} = \frac{-1}{60}$.

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) $\hspace{10px}n\neq 0 \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

To sum up, the lcm of 30 and 20 is 60. In common notation: lcm (30,20) = 60.

If you have been searching for lcm 30 and 20 or lcm 30 20 then you have come to the correct page, too. The same is the true if you typed lcm for 30 and 20 in your favorite search engine.

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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