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# LCM of 45 and 30

The lcm of 45 and 30 is the smallest positive integer that divides the numbers 45 and 30 without a remainder. Spelled out, it is the least common multiple of 45 and 30. Here you can find the lcm of 45 and 30, along with a total of three methods for computing it.

90

In addition, we have a calculator you should check out. Not only can it determine the lcm of 45 and 30, but also that of three or more integers including forty-five and thirty for example. Keep reading to learn everything about the lcm (45,30) and the terms related to it.

## What is the LCM of 45 and 30

If you just want to know what is the least common multiple of 45 and 30, it is 90. Usually, this is written as

lcm(45,30) = 90

The lcm of 45 and 30 can be obtained like this:

• The multiples of 45 are … , 45, 90, 135, ….
• The multiples of 30 are …, 60, 90, 120, …
• The common multiples of 45 and 30 are n x 90, intersecting the two sets above, .
• In the intersection multiples of 45 ∩ multiples of 30 the least positive element is 90.
• Therefore, the least common multiple of 45 and 30 is 90.

Taking the above into account you also know how to find all the common multiples of 45 and 30, not just the smallest. In the next section we show you how to calculate the lcm of forty-five and thirty by means of two more methods.

## How to find the LCM of 45 and 30

The least common multiple of 45 and 30 can be computed by using the greatest common factor aka gcf of 45 and 30. This is the easiest approach:

lcm (45,30) = = 90

Alternatively, the lcm of 45 and 30 can be found using the prime factorization of 45 and 30:

• The prime factorization of 45 is: 3 x 3 x 5
• The prime factorization of 30 is: 2 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(45,45) = 90

In any case, the easiest way to compute the lcm of two numbers like 45 and 30 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 45,30. Push the button only to start over.

Similar searched terms on our site also include:

## Use of LCM of 45 and 30

What is the least common multiple of 45 and 30 used for? Answer: It is helpful for adding and subtracting fractions like 1/45 and 1/30. Just multiply the dividends and divisors by 2 and 3, respectively, such that the divisors have the value of 90, the lcm of 45 and 30.

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## Properties of LCM of 45 and 30

The most important properties of the lcm(45,30) are:

• Commutative property: lcm(45,30) = lcm(30,45)
• Associative property: lcm(45,30,n) = lcm(lcm(30,45),n)

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 30 is 90. In common notation: lcm (45,30) = 90.

If you have been searching for lcm 45 and 30 or lcm 45 30 then you have come to the correct page, too. The same is the true if you typed lcm for 45 and 30 in your favorite search engine.

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

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