What is the LCM of 45 and 113?

Solution: The LCM of 45 and 113 is 5085

Methods

How to find the LCM of 45 and 113 using Prime Factorization

One way to find the LCM of 45 and 113 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:

Here is the prime factorization of 45:

3^2 × 5^1

And this is the prime factorization of 113:

113^1

When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 3, 5, 113

3^2 × 5^1 × 113^1 = 5085

Through this we see that the LCM of 45 and 113 is 5085.

How to Find the LCM of 45 and 113 by Listing Common Multiples

The first step to this method of finding the Least Common Multiple of 45 and 113 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.

Let’s take a look at the multiples for each of these numbers, 45 and 113:

What are the Multiples of 45?

What are the Multiples of 113?

Let’s take a look at the first 10 multiples for each of these numbers, 45 and 113:

First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450

First 10 Multiples of 113: 113, 226, 339, 452, 565, 678, 791, 904, 1017, 1130

You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 45 and 113 are 5085, 10170, 15255. Because 5085 is the smallest, it is the least common multiple.

The LCM of 45 and 113 is 5085.

Find the LCM of Other Number Pairs

Want more practice? Try some of these other LCM problems:

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