Solution: The LCM of 31 and 120 is 3720
Methods
How to find the LCM of 31 and 120 using Prime Factorization
One way to find the LCM of 31 and 120 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 31?
What are the Factors of 120?
Here is the prime factorization of 31:
3
1
1
31^1
3 1 1
And this is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 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: 31, 2, 3, 5
2
3
×
3
1
×
5
1
×
3
1
1
=
3720
2^3 × 3^1 × 5^1 × 31^1 = 3720
2 3 × 3 1 × 5 1 × 3 1 1 = 3720
Through this we see that the LCM of 31 and 120 is 3720.
How to Find the LCM of 31 and 120 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 31 and 120 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, 31 and 120:
What are the Multiples of 31?
What are the Multiples of 120?
Let’s take a look at the first 10 multiples for each of these numbers, 31 and 120:
First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310
First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200
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 31 and 120 are 3720, 7440, 11160. Because 3720 is the smallest, it is the least common multiple.
The LCM of 31 and 120 is 3720.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 102 and 10?
What is the LCM of 138 and 36?
What is the LCM of 89 and 110?
What is the LCM of 92 and 93?
What is the LCM of 126 and 111?