Solution: The LCM of 72 and 27 is 216
Methods
How to find the LCM of 72 and 27 using Prime Factorization
One way to find the LCM of 72 and 27 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 27?
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 27:
3
3
3^3
3 3
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
2
3
×
3
3
=
216
2^3 × 3^3 = 216
2 3 × 3 3 = 216
Through this we see that the LCM of 72 and 27 is 216.
How to Find the LCM of 72 and 27 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 72 and 27 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 27:
What are the Multiples of 72?
What are the Multiples of 27?
Let’s take a look at the first 10 multiples for each of these numbers, 72 and 27:
First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720
First 10 Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270
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 27 are 216, 432, 648. Because 216 is the smallest, it is the least common multiple.
The LCM of 72 and 27 is 216.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 28 and 150?
What is the LCM of 89 and 143?
What is the LCM of 90 and 40?
What is the LCM of 66 and 88?
What is the LCM of 123 and 14?