Solution: The LCM of 60 and 53 is 3180
Methods
How to find the LCM of 60 and 53 using Prime Factorization
One way to find the LCM of 60 and 53 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 53?
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 53:
5
3
1
53^1
5 3 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, 53
2
2
×
3
1
×
5
1
×
5
3
1
=
3180
2^2 × 3^1 × 5^1 × 53^1 = 3180
2 2 × 3 1 × 5 1 × 5 3 1 = 3180
Through this we see that the LCM of 60 and 53 is 3180.
How to Find the LCM of 60 and 53 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 60 and 53 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 53:
What are the Multiples of 60?
What are the Multiples of 53?
Let’s take a look at the first 10 multiples for each of these numbers, 60 and 53:
First 10 Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600
First 10 Multiples of 53: 53, 106, 159, 212, 265, 318, 371, 424, 477, 530
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 53 are 3180, 6360, 9540. Because 3180 is the smallest, it is the least common multiple.
The LCM of 60 and 53 is 3180.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 6 and 134?
What is the LCM of 126 and 21?
What is the LCM of 33 and 113?
What is the LCM of 53 and 45?
What is the LCM of 76 and 129?