Solution: The LCM of 31 and 89 is 2759
Methods
How to find the LCM of 31 and 89 using Prime Factorization
One way to find the LCM of 31 and 89 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 89?
Here is the prime factorization of 31:
3
1
1
31^1
3 1 1
And this is the prime factorization of 89:
8
9
1
89^1
8 9 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, 89
3
1
1
×
8
9
1
=
2759
31^1 × 89^1 = 2759
3 1 1 × 8 9 1 = 2759
Through this we see that the LCM of 31 and 89 is 2759.
How to Find the LCM of 31 and 89 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 31 and 89 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 89:
What are the Multiples of 31?
What are the Multiples of 89?
Let’s take a look at the first 10 multiples for each of these numbers, 31 and 89:
First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310
First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890
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 89 are 2759, 5518, 8277. Because 2759 is the smallest, it is the least common multiple.
The LCM of 31 and 89 is 2759.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 65 and 142?
What is the LCM of 148 and 99?
What is the LCM of 44 and 34?
What is the LCM of 136 and 9?
What is the LCM of 143 and 40?