Solution: The LCM of 75 and 60 is 300
Methods
How to find the LCM of 75 and 60 using Prime Factorization
One way to find the LCM of 75 and 60 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 75?
What are the Factors of 60?
Here is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
And this is the prime factorization of 60:
2
2
×
3
1
×
5
1
2^2 × 3^1 × 5^1
2 2 × 3 1 × 5 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: 3, 5, 2
2
2
×
3
1
×
5
2
=
300
2^2 × 3^1 × 5^2 = 300
2 2 × 3 1 × 5 2 = 300
Through this we see that the LCM of 75 and 60 is 300.
How to Find the LCM of 75 and 60 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 75 and 60 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, 75 and 60:
What are the Multiples of 75?
What are the Multiples of 60?
Let’s take a look at the first 10 multiples for each of these numbers, 75 and 60:
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
First 10 Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600
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 75 and 60 are 300, 600, 900. Because 300 is the smallest, it is the least common multiple.
The LCM of 75 and 60 is 300.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 51 and 123?
What is the LCM of 22 and 120?
What is the LCM of 3 and 10?
What is the LCM of 58 and 72?
What is the LCM of 65 and 29?