Solution: The LCM of 108 and 39 is 1404
Methods
How to find the LCM of 108 and 39 using Prime Factorization
One way to find the LCM of 108 and 39 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 39?
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 39:
3
1
×
1
3
1
3^1 × 13^1
3 1 × 1 3 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, 13
2
2
×
3
3
×
1
3
1
=
1404
2^2 × 3^3 × 13^1 = 1404
2 2 × 3 3 × 1 3 1 = 1404
Through this we see that the LCM of 108 and 39 is 1404.
How to Find the LCM of 108 and 39 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 108 and 39 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 39:
What are the Multiples of 108?
What are the Multiples of 39?
Let’s take a look at the first 10 multiples for each of these numbers, 108 and 39:
First 10 Multiples of 108: 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080
First 10 Multiples of 39: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390
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 39 are 1404, 2808, 4212. Because 1404 is the smallest, it is the least common multiple.
The LCM of 108 and 39 is 1404.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 76 and 57?
What is the LCM of 21 and 18?
What is the LCM of 135 and 60?
What is the LCM of 23 and 40?
What is the LCM of 93 and 31?