Solution: The LCM of 7 and 31 is 217
Methods
How to find the LCM of 7 and 31 using Prime Factorization
One way to find the LCM of 7 and 31 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 7?
What are the Factors of 31?
Here is the prime factorization of 7:
7
1
7^1
7 1
And this is the prime factorization of 31:
3
1
1
31^1
3 1 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: 7, 31
7
1
×
3
1
1
=
217
7^1 × 31^1 = 217
7 1 × 3 1 1 = 217
Through this we see that the LCM of 7 and 31 is 217.
How to Find the LCM of 7 and 31 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 7 and 31 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, 7 and 31:
What are the Multiples of 7?
What are the Multiples of 31?
Let’s take a look at the first 10 multiples for each of these numbers, 7 and 31:
First 10 Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310
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 7 and 31 are 217, 434, 651. Because 217 is the smallest, it is the least common multiple.
The LCM of 7 and 31 is 217.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 45 and 51?
What is the LCM of 27 and 124?
What is the LCM of 91 and 80?
What is the LCM of 77 and 126?
What is the LCM of 37 and 131?