LCM of 45 and 36


The lcm of 45 and 36 is the smallest positive integer that divides the numbers 45 and 36 without a remainder. Spelled out, it is the least common multiple of 45 and 36. Here you can find the lcm of 45 and 36, 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 45 and 36, but also that of three or more integers including forty-five and thirty-six for example. Keep reading to learn everything about the lcm (45,36) and the terms related to it.

What is the LCM of 45 and 36

If you just want to know what is the least common multiple of 45 and 36, it is 180. Usually, this is written as

lcm(45,36) = 180

The lcm of 45 and 36 can be obtained like this:

  • The multiples of 45 are …, 135, 180, 225, ….
  • The multiples of 36 are …, 144, 180, 216, …
  • The common multiples of 45 and 36 are n x 180, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 45 ∩ multiples of 36 the least positive element is 180.
  • Therefore, the least common multiple of 45 and 36 is 180.

Taking the above into account you also know how to find all the common multiples of 45 and 36, not just the smallest. In the next section we show you how to calculate the lcm of forty-five and thirty-six by means of two more methods.

How to find the LCM of 45 and 36

The least common multiple of 45 and 36 can be computed by using the greatest common factor aka gcf of 45 and 36. This is the easiest approach:

lcm (45,36) = $\frac{45 \times 36}{gcf(45,36)} = \frac{1620}{9}$ = 180

Alternatively, the lcm of 45 and 36 can be found using the prime factorization of 45 and 36:

  • The prime factorization of 45 is: 3 x 3 x 5
  • The prime factorization of 36 is: 2 x 2 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(45,45) = 180

In any case, the easiest way to compute the lcm of two numbers like 45 and 36 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 45,36. Push the button only to start over.

The lcm is...
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Use of LCM of 45 and 36

What is the least common multiple of 45 and 36 used for? Answer: It is helpful for adding and subtracting fractions like 1/45 and 1/36. Just multiply the dividends and divisors by 4 and 5, respectively, such that the divisors have the value of 180, the lcm of 45 and 36.

$\frac{1}{45} + \frac{1}{36} = \frac{4}{180} + \frac{5}{180} = \frac{9}{180}$. $\hspace{30px}\frac{1}{45} – \frac{1}{36} = \frac{4}{180} – \frac{5}{180} = \frac{-1}{180}$.

Properties of LCM of 45 and 36

The most important properties of the lcm(45,36) are:

  • Commutative property: lcm(45,36) = lcm(36,45)
  • Associative property: lcm(45,36,n) = lcm(lcm(36,45),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 45 and 36 is 180. In common notation: lcm (45,36) = 180.

If you have been searching for lcm 45 and 36 or lcm 45 36 then you have come to the correct page, too. The same is the true if you typed lcm for 45 and 36 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including forty-five / thirty-six by using the search form in the sidebar of this page.

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