Solution: The LCM of 31 and 68 is 2108
Methods
How to find the LCM of 31 and 68 using Prime Factorization
One way to find the LCM of 31 and 68 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 68?
Here is the prime factorization of 31:
3
1
1
31^1
3 1 1
And this is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 1 7 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, 17
2
2
×
1
7
1
×
3
1
1
=
2108
2^2 × 17^1 × 31^1 = 2108
2 2 × 1 7 1 × 3 1 1 = 2108
Through this we see that the LCM of 31 and 68 is 2108.
How to Find the LCM of 31 and 68 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 31 and 68 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 68:
What are the Multiples of 31?
What are the Multiples of 68?
Let’s take a look at the first 10 multiples for each of these numbers, 31 and 68:
First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310
First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680
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 68 are 2108, 4216, 6324. Because 2108 is the smallest, it is the least common multiple.
The LCM of 31 and 68 is 2108.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 149 and 65?
What is the LCM of 77 and 3?
What is the LCM of 81 and 109?
What is the LCM of 147 and 141?
What is the LCM of 26 and 137?