Solution: The LCM of 93 and 108 is 3348
Methods
How to find the LCM of 93 and 108 using Prime Factorization
One way to find the LCM of 93 and 108 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 93?
What are the Factors of 108?
Here is the prime factorization of 93:
3
1
×
3
1
1
3^1 × 31^1
3 1 × 3 1 1
And this is the prime factorization of 108:
2
2
×
3
3
2^2 × 3^3
2 2 × 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: 3, 31, 2
2
2
×
3
3
×
3
1
1
=
3348
2^2 × 3^3 × 31^1 = 3348
2 2 × 3 3 × 3 1 1 = 3348
Through this we see that the LCM of 93 and 108 is 3348.
How to Find the LCM of 93 and 108 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 93 and 108 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, 93 and 108:
What are the Multiples of 93?
What are the Multiples of 108?
Let’s take a look at the first 10 multiples for each of these numbers, 93 and 108:
First 10 Multiples of 93: 93, 186, 279, 372, 465, 558, 651, 744, 837, 930
First 10 Multiples of 108: 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080
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 93 and 108 are 3348, 6696, 10044. Because 3348 is the smallest, it is the least common multiple.
The LCM of 93 and 108 is 3348.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 120 and 56?
What is the LCM of 54 and 87?
What is the LCM of 11 and 136?
What is the LCM of 112 and 122?
What is the LCM of 83 and 147?