Solution: The LCM of 60 and 131 is 7860
Methods
How to find the LCM of 60 and 131 using Prime Factorization
One way to find the LCM of 60 and 131 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 60?
What are the Factors of 131?
Here is the prime factorization of 60:
2
2
×
3
1
×
5
1
2^2 × 3^1 × 5^1
2 2 × 3 1 × 5 1
And this is the prime factorization of 131:
13
1
1
131^1
13 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: 2, 3, 5, 131
2
2
×
3
1
×
5
1
×
13
1
1
=
7860
2^2 × 3^1 × 5^1 × 131^1 = 7860
2 2 × 3 1 × 5 1 × 13 1 1 = 7860
Through this we see that the LCM of 60 and 131 is 7860.
How to Find the LCM of 60 and 131 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 60 and 131 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, 60 and 131:
What are the Multiples of 60?
What are the Multiples of 131?
Let’s take a look at the first 10 multiples for each of these numbers, 60 and 131:
First 10 Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600
First 10 Multiples of 131: 131, 262, 393, 524, 655, 786, 917, 1048, 1179, 1310
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 60 and 131 are 7860, 15720, 23580. Because 7860 is the smallest, it is the least common multiple.
The LCM of 60 and 131 is 7860.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 62 and 78?
What is the LCM of 96 and 88?
What is the LCM of 5 and 86?
What is the LCM of 1 and 14?
What is the LCM of 138 and 35?