Solution: The LCM of 108 and 59 is 6372
Methods
How to find the LCM of 108 and 59 using Prime Factorization
One way to find the LCM of 108 and 59 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 108?
What are the Factors of 59?
Here is the prime factorization of 108:
2
2
×
3
3
2^2 × 3^3
2 2 × 3 3
And this is the prime factorization of 59:
5
9
1
59^1
5 9 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: 2, 3, 59
2
2
×
3
3
×
5
9
1
=
6372
2^2 × 3^3 × 59^1 = 6372
2 2 × 3 3 × 5 9 1 = 6372
Through this we see that the LCM of 108 and 59 is 6372.
How to Find the LCM of 108 and 59 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 108 and 59 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, 108 and 59:
What are the Multiples of 108?
What are the Multiples of 59?
Let’s take a look at the first 10 multiples for each of these numbers, 108 and 59:
First 10 Multiples of 108: 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080
First 10 Multiples of 59: 59, 118, 177, 236, 295, 354, 413, 472, 531, 590
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 108 and 59 are 6372, 12744, 19116. Because 6372 is the smallest, it is the least common multiple.
The LCM of 108 and 59 is 6372.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 98 and 117?
What is the LCM of 55 and 63?
What is the LCM of 134 and 54?
What is the LCM of 72 and 51?
What is the LCM of 57 and 112?