Solution: The LCM of 138 and 116 is 8004
Methods
How to find the LCM of 138 and 116 using Prime Factorization
One way to find the LCM of 138 and 116 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 138?
What are the Factors of 116?
Here 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
And this is the prime factorization of 116:
2
2
×
2
9
1
2^2 × 29^1
2 2 × 2 9 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, 23, 29
2
2
×
3
1
×
2
3
1
×
2
9
1
=
8004
2^2 × 3^1 × 23^1 × 29^1 = 8004
2 2 × 3 1 × 2 3 1 × 2 9 1 = 8004
Through this we see that the LCM of 138 and 116 is 8004.
How to Find the LCM of 138 and 116 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 138 and 116 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, 138 and 116:
What are the Multiples of 138?
What are the Multiples of 116?
Let’s take a look at the first 10 multiples for each of these numbers, 138 and 116:
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
First 10 Multiples of 116: 116, 232, 348, 464, 580, 696, 812, 928, 1044, 1160
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 138 and 116 are 8004, 16008, 24012. Because 8004 is the smallest, it is the least common multiple.
The LCM of 138 and 116 is 8004.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 72 and 74?
What is the LCM of 91 and 69?
What is the LCM of 116 and 31?
What is the LCM of 39 and 106?
What is the LCM of 41 and 145?