Solution: The LCM of 117 and 15 is 585
Methods
How to find the LCM of 117 and 15 using Prime Factorization
One way to find the LCM of 117 and 15 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:
What are the Factors of 117?
What are the Factors of 15?
Here is the prime factorization of 117:
3
2
×
1
3
1
3^2 × 13^1
3 2 × 1 3 1
And this is the prime factorization of 15:
3
1
×
5
1
3^1 × 5^1
3 1 × 5 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, 13, 5
3
2
×
5
1
×
1
3
1
=
585
3^2 × 5^1 × 13^1 = 585
3 2 × 5 1 × 1 3 1 = 585
Through this we see that the LCM of 117 and 15 is 585.
How to Find the LCM of 117 and 15 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 117 and 15 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, 117 and 15:
What are the Multiples of 117?
What are the Multiples of 15?
Let’s take a look at the first 10 multiples for each of these numbers, 117 and 15:
First 10 Multiples of 117: 117, 234, 351, 468, 585, 702, 819, 936, 1053, 1170
First 10 Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150
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 117 and 15 are 585, 1170, 1755. Because 585 is the smallest, it is the least common multiple.
The LCM of 117 and 15 is 585.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 109 and 44?
What is the LCM of 98 and 126?
What is the LCM of 4 and 18?
What is the LCM of 52 and 110?
What is the LCM of 2 and 24?