Solution: The LCM of 93 and 138 is 4278
Methods
How to find the LCM of 93 and 138 using Prime Factorization
One way to find the LCM of 93 and 138 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 138?
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 138:
2
1
×
3
1
×
2
3
1
2^1 × 3^1 × 23^1
2 1 × 3 1 × 2 3 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: 3, 31, 2, 23
2
1
×
3
1
×
2
3
1
×
3
1
1
=
4278
2^1 × 3^1 × 23^1 × 31^1 = 4278
2 1 × 3 1 × 2 3 1 × 3 1 1 = 4278
Through this we see that the LCM of 93 and 138 is 4278.
How to Find the LCM of 93 and 138 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 93 and 138 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 138:
What are the Multiples of 93?
What are the Multiples of 138?
Let’s take a look at the first 10 multiples for each of these numbers, 93 and 138:
First 10 Multiples of 93: 93, 186, 279, 372, 465, 558, 651, 744, 837, 930
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
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 138 are 4278, 8556, 12834. Because 4278 is the smallest, it is the least common multiple.
The LCM of 93 and 138 is 4278.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 83 and 79?
What is the LCM of 36 and 135?
What is the LCM of 10 and 126?
What is the LCM of 129 and 121?
What is the LCM of 58 and 2?