Solution: The LCM of 72 and 30 is 360
Methods
How to find the LCM of 72 and 30 using Prime Factorization
One way to find the LCM of 72 and 30 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 30?
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 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 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, 3, 5
2
3
×
3
2
×
5
1
=
360
2^3 × 3^2 × 5^1 = 360
2 3 × 3 2 × 5 1 = 360
Through this we see that the LCM of 72 and 30 is 360.
How to Find the LCM of 72 and 30 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 72 and 30 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 30:
What are the Multiples of 72?
What are the Multiples of 30?
Let’s take a look at the first 10 multiples for each of these numbers, 72 and 30:
First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
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 30 are 360, 720, 1080. Because 360 is the smallest, it is the least common multiple.
The LCM of 72 and 30 is 360.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 128 and 12?
What is the LCM of 111 and 21?
What is the LCM of 74 and 85?
What is the LCM of 91 and 133?
What is the LCM of 108 and 150?