LCM of 90 and 54


The lcm of 90 and 54 is the smallest positive integer that divides the numbers 90 and 54 without a remainder. Spelled out, it is the least common multiple of 90 and 54. Here you can find the lcm of 90 and 54, 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 90 and 54, but also that of three or more integers including ninety and fifty-four for example. Keep reading to learn everything about the lcm (90,54) and the terms related to it.

What is the LCM of 90 and 54

If you just want to know what is the least common multiple of 90 and 54, it is 270. Usually, this is written as

lcm(90,54) = 270

The lcm of 90 and 54 can be obtained like this:

  • The multiples of 90 are …, 180, 270, 360, ….
  • The multiples of 54 are …, 216, 270, 324, …
  • The common multiples of 90 and 54 are n x 270, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 90 ∩ multiples of 54 the least positive element is 270.
  • Therefore, the least common multiple of 90 and 54 is 270.

Taking the above into account you also know how to find all the common multiples of 90 and 54, not just the smallest. In the next section we show you how to calculate the lcm of ninety and fifty-four by means of two more methods.

How to find the LCM of 90 and 54

The least common multiple of 90 and 54 can be computed by using the greatest common factor aka gcf of 90 and 54. This is the easiest approach:

lcm (90,54) = $\frac{90 \times 54}{gcf(90,54)} = \frac{4860}{18}$ = 270

Alternatively, the lcm of 90 and 54 can be found using the prime factorization of 90 and 54:

  • The prime factorization of 90 is: 2 x 3 x 3 x 5
  • The prime factorization of 54 is: 2 x 3 x 3 x 3
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(90,90) = 270

In any case, the easiest way to compute the lcm of two numbers like 90 and 54 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 90,54. Push the button only to start over.

The lcm is...
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Use of LCM of 90 and 54

What is the least common multiple of 90 and 54 used for? Answer: It is helpful for adding and subtracting fractions like 1/90 and 1/54. Just multiply the dividends and divisors by 3 and 5, respectively, such that the divisors have the value of 270, the lcm of 90 and 54.

$\frac{1}{90} + \frac{1}{54} = \frac{3}{270} + \frac{5}{270} = \frac{8}{270}$. $\hspace{30px}\frac{1}{90} – \frac{1}{54} = \frac{3}{270} – \frac{5}{270} = \frac{-2}{270}$.

Properties of LCM of 90 and 54

The most important properties of the lcm(90,54) are:

  • Commutative property: lcm(90,54) = lcm(54,90)
  • Associative property: lcm(90,54,n) = lcm(lcm(54,90),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 90 and 54 is 270. In common notation: lcm (90,54) = 270.

If you have been searching for lcm 90 and 54 or lcm 90 54 then you have come to the correct page, too. The same is the true if you typed lcm for 90 and 54 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including ninety / fifty-four by using the search form in the sidebar of this page.

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