Solution: The LCM of 72 and 97 is 6984
Methods
How to find the LCM of 72 and 97 using Prime Factorization
One way to find the LCM of 72 and 97 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 97?
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 97:
9
7
1
97^1
9 7 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, 97
2
3
×
3
2
×
9
7
1
=
6984
2^3 × 3^2 × 97^1 = 6984
2 3 × 3 2 × 9 7 1 = 6984
Through this we see that the LCM of 72 and 97 is 6984.
How to Find the LCM of 72 and 97 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 72 and 97 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 97:
What are the Multiples of 72?
What are the Multiples of 97?
Let’s take a look at the first 10 multiples for each of these numbers, 72 and 97:
First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720
First 10 Multiples of 97: 97, 194, 291, 388, 485, 582, 679, 776, 873, 970
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 97 are 6984, 13968, 20952. Because 6984 is the smallest, it is the least common multiple.
The LCM of 72 and 97 is 6984.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 25 and 149?
What is the LCM of 148 and 93?
What is the LCM of 141 and 12?
What is the LCM of 60 and 88?
What is the LCM of 2 and 54?