Solution: The LCM of 12 and 75 is 300
Methods
How to find the LCM of 12 and 75 using Prime Factorization
One way to find the LCM of 12 and 75 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 12?
What are the Factors of 75?
Here is the prime factorization of 12:
2
2
×
3
1
2^2 × 3^1
2 2 × 3 1
And this is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
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
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 12 and 75 is 300.
How to Find the LCM of 12 and 75 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 12 and 75 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, 12 and 75:
What are the Multiples of 12?
What are the Multiples of 75?
Let’s take a look at the first 10 multiples for each of these numbers, 12 and 75:
First 10 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
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 12 and 75 are 300, 600, 900. Because 300 is the smallest, it is the least common multiple.
The LCM of 12 and 75 is 300.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 29 and 116?
What is the LCM of 130 and 28?
What is the LCM of 25 and 6?
What is the LCM of 96 and 7?
What is the LCM of 39 and 73?