Solution: The LCM of 131 and 137 is 17947
Methods
How to find the LCM of 131 and 137 using Prime Factorization
One way to find the LCM of 131 and 137 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 131?
What are the Factors of 137?
Here is the prime factorization of 131:
13
1
1
131^1
13 1 1
And this is the prime factorization of 137:
13
7
1
137^1
13 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: 131, 137
13
1
1
×
13
7
1
=
17947
131^1 × 137^1 = 17947
13 1 1 × 13 7 1 = 17947
Through this we see that the LCM of 131 and 137 is 17947.
How to Find the LCM of 131 and 137 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 131 and 137 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, 131 and 137:
What are the Multiples of 131?
What are the Multiples of 137?
Let’s take a look at the first 10 multiples for each of these numbers, 131 and 137:
First 10 Multiples of 131: 131, 262, 393, 524, 655, 786, 917, 1048, 1179, 1310
First 10 Multiples of 137: 137, 274, 411, 548, 685, 822, 959, 1096, 1233, 1370
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 131 and 137 are 17947, 35894, 53841. Because 17947 is the smallest, it is the least common multiple.
The LCM of 131 and 137 is 17947.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 148 and 70?
What is the LCM of 21 and 23?
What is the LCM of 74 and 48?
What is the LCM of 93 and 12?
What is the LCM of 73 and 10?