LCM of 90 and 8


The lcm of 90 and 8 is the smallest positive integer that divides the numbers 90 and 8 without a remainder. Spelled out, it is the least common multiple of 90 and 8. Here you can find the lcm of 90 and 8, 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 8, but also that of three or more integers including ninety and eight for example. Keep reading to learn everything about the lcm (90,8) and the terms related to it.

What is the LCM of 90 and 8

If you just want to know what is the least common multiple of 90 and 8, it is 360. Usually, this is written as

lcm(90,8) = 360

The lcm of 90 and 8 can be obtained like this:

  • The multiples of 90 are …, 270, 360, 450, ….
  • The multiples of 8 are …, 352, 360, 368, …
  • The common multiples of 90 and 8 are n x 360, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 90 ∩ multiples of 8 the least positive element is 360.
  • Therefore, the least common multiple of 90 and 8 is 360.

Taking the above into account you also know how to find all the common multiples of 90 and 8, not just the smallest. In the next section we show you how to calculate the lcm of ninety and eight by means of two more methods.

How to find the LCM of 90 and 8

The least common multiple of 90 and 8 can be computed by using the greatest common factor aka gcf of 90 and 8. This is the easiest approach:

lcm (90,8) = $\frac{90 \times 8}{gcf(90,8)} = \frac{720}{2}$ = 360

Alternatively, the lcm of 90 and 8 can be found using the prime factorization of 90 and 8:

  • The prime factorization of 90 is: 2 x 3 x 3 x 5
  • The prime factorization of 8 is: 2 x 2 x 2
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(90,90) = 360

In any case, the easiest way to compute the lcm of two numbers like 90 and 8 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 90,8. Push the button only to start over.

The lcm is...
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Use of LCM of 90 and 8

What is the least common multiple of 90 and 8 used for? Answer: It is helpful for adding and subtracting fractions like 1/90 and 1/8. Just multiply the dividends and divisors by 4 and 45, respectively, such that the divisors have the value of 360, the lcm of 90 and 8.

$\frac{1}{90} + \frac{1}{8} = \frac{4}{360} + \frac{45}{360} = \frac{49}{360}$. $\hspace{30px}\frac{1}{90} – \frac{1}{8} = \frac{4}{360} – \frac{45}{360} = \frac{-41}{360}$.

Properties of LCM of 90 and 8

The most important properties of the lcm(90,8) are:

  • Commutative property: lcm(90,8) = lcm(8,90)
  • Associative property: lcm(90,8,n) = lcm(lcm(8,90),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 8 is 360. In common notation: lcm (90,8) = 360.

If you have been searching for lcm 90 and 8 or lcm 90 8 then you have come to the correct page, too. The same is the true if you typed lcm for 90 and 8 in your favorite search engine.

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

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