Solution: The LCM of 76 and 120 is 2280
Methods
How to find the LCM of 76 and 120 using Prime Factorization
One way to find the LCM of 76 and 120 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 76?
What are the Factors of 120?
Here is the prime factorization of 76:
2
2
×
1
9
1
2^2 × 19^1
2 2 × 1 9 1
And this is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 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: 2, 19, 3, 5
2
3
×
3
1
×
5
1
×
1
9
1
=
2280
2^3 × 3^1 × 5^1 × 19^1 = 2280
2 3 × 3 1 × 5 1 × 1 9 1 = 2280
Through this we see that the LCM of 76 and 120 is 2280.
How to Find the LCM of 76 and 120 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 76 and 120 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, 76 and 120:
What are the Multiples of 76?
What are the Multiples of 120?
Let’s take a look at the first 10 multiples for each of these numbers, 76 and 120:
First 10 Multiples of 76: 76, 152, 228, 304, 380, 456, 532, 608, 684, 760
First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200
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 76 and 120 are 2280, 4560, 6840. Because 2280 is the smallest, it is the least common multiple.
The LCM of 76 and 120 is 2280.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 55 and 93?
What is the LCM of 150 and 22?
What is the LCM of 88 and 123?
What is the LCM of 44 and 132?
What is the LCM of 26 and 120?