Solution: The LCM of 72 and 80 is 720
Methods
How to find the LCM of 72 and 80 using Prime Factorization
One way to find the LCM of 72 and 80 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 72?
What are the Factors of 80?
Here is the prime factorization of 72:
2
3
×
3
2
2^3 × 3^2
2 3 × 3 2
And this is the prime factorization of 80:
2
4
×
5
1
2^4 × 5^1
2 4 × 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, 3, 5
2
4
×
3
2
×
5
1
=
720
2^4 × 3^2 × 5^1 = 720
2 4 × 3 2 × 5 1 = 720
Through this we see that the LCM of 72 and 80 is 720.
How to Find the LCM of 72 and 80 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 72 and 80 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, 72 and 80:
What are the Multiples of 72?
What are the Multiples of 80?
Let’s take a look at the first 10 multiples for each of these numbers, 72 and 80:
First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720
First 10 Multiples of 80: 80, 160, 240, 320, 400, 480, 560, 640, 720, 800
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 72 and 80 are 720, 1440, 2160. Because 720 is the smallest, it is the least common multiple.
The LCM of 72 and 80 is 720.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 44 and 149?
What is the LCM of 128 and 96?
What is the LCM of 85 and 91?
What is the LCM of 35 and 22?
What is the LCM of 106 and 52?