Solution: The LCM of 76 and 20 is 380
Methods
How to find the LCM of 76 and 20 using Prime Factorization
One way to find the LCM of 76 and 20 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 20?
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 20:
2
2
×
5
1
2^2 × 5^1
2 2 × 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, 5
2
2
×
5
1
×
1
9
1
=
380
2^2 × 5^1 × 19^1 = 380
2 2 × 5 1 × 1 9 1 = 380
Through this we see that the LCM of 76 and 20 is 380.
How to Find the LCM of 76 and 20 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 76 and 20 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 20:
What are the Multiples of 76?
What are the Multiples of 20?
Let’s take a look at the first 10 multiples for each of these numbers, 76 and 20:
First 10 Multiples of 76: 76, 152, 228, 304, 380, 456, 532, 608, 684, 760
First 10 Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200
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 20 are 380, 760, 1140. Because 380 is the smallest, it is the least common multiple.
The LCM of 76 and 20 is 380.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 4 and 2?
What is the LCM of 102 and 132?
What is the LCM of 21 and 30?
What is the LCM of 118 and 113?
What is the LCM of 97 and 130?