Solution: The LCM of 31 and 67 is 2077
Methods
How to find the LCM of 31 and 67 using Prime Factorization
One way to find the LCM of 31 and 67 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 67?
Here is the prime factorization of 31:
3
1
1
31^1
3 1 1
And this is the prime factorization of 67:
6
7
1
67^1
6 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, 67
3
1
1
×
6
7
1
=
2077
31^1 × 67^1 = 2077
3 1 1 × 6 7 1 = 2077
Through this we see that the LCM of 31 and 67 is 2077.
How to Find the LCM of 31 and 67 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 31 and 67 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 67:
What are the Multiples of 31?
What are the Multiples of 67?
Let’s take a look at the first 10 multiples for each of these numbers, 31 and 67:
First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310
First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670
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 67 are 2077, 4154, 6231. Because 2077 is the smallest, it is the least common multiple.
The LCM of 31 and 67 is 2077.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 111 and 75?
What is the LCM of 145 and 51?
What is the LCM of 93 and 63?
What is the LCM of 85 and 8?
What is the LCM of 124 and 37?