LCM of 72 and 90


The lcm of 72 and 90 is the smallest positive integer that divides the numbers 72 and 90 without a remainder. Spelled out, it is the least common multiple of 72 and 90. Here you can find the lcm of 72 and 90, 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 72 and 90, but also that of three or more integers including seventy-two and ninety for example. Keep reading to learn everything about the lcm (72,90) and the terms related to it.

What is the LCM of 72 and 90

If you just want to know what is the least common multiple of 72 and 90, it is 360. Usually, this is written as

lcm(72,90) = 360

The lcm of 72 and 90 can be obtained like this:

  • The multiples of 72 are …, 288, 360, 432, ….
  • The multiples of 90 are …, 270, 360, 450, …
  • The common multiples of 72 and 90 are n x 360, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 72 ∩ multiples of 90 the least positive element is 360.
  • Therefore, the least common multiple of 72 and 90 is 360.

Taking the above into account you also know how to find all the common multiples of 72 and 90, not just the smallest. In the next section we show you how to calculate the lcm of seventy-two and ninety by means of two more methods.

How to find the LCM of 72 and 90

The least common multiple of 72 and 90 can be computed by using the greatest common factor aka gcf of 72 and 90. This is the easiest approach:

lcm (72,90) = $\frac{72 \times 90}{gcf(72,90)} = \frac{6480}{18}$ = 360

Alternatively, the lcm of 72 and 90 can be found using the prime factorization of 72 and 90:

  • The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3
  • The prime factorization of 90 is: 2 x 3 x 3 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(72,72) = 360

In any case, the easiest way to compute the lcm of two numbers like 72 and 90 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 72,90. Push the button only to start over.

The lcm is...
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Use of LCM of 72 and 90

What is the least common multiple of 72 and 90 used for? Answer: It is helpful for adding and subtracting fractions like 1/72 and 1/90. Just multiply the dividends and divisors by 5 and 4, respectively, such that the divisors have the value of 360, the lcm of 72 and 90.

$\frac{1}{72} + \frac{1}{90} = \frac{5}{360} + \frac{4}{360} = \frac{9}{360}$. $\hspace{30px}\frac{1}{72} – \frac{1}{90} = \frac{5}{360} – \frac{4}{360} = \frac{1}{360}$.

Properties of LCM of 72 and 90

The most important properties of the lcm(72,90) are:

  • Commutative property: lcm(72,90) = lcm(90,72)
  • Associative property: lcm(72,90,n) = lcm(lcm(90,72),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 72 and 90 is 360. In common notation: lcm (72,90) = 360.

If you have been searching for lcm 72 and 90 or lcm 72 90 then you have come to the correct page, too. The same is the true if you typed lcm for 72 and 90 in your favorite search engine.

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

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