Solution: The LCM of 138 and 37 is 5106
Methods
How to find the LCM of 138 and 37 using Prime Factorization
One way to find the LCM of 138 and 37 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 37?
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 37:
3
7
1
37^1
3 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, 23, 37
2
1
×
3
1
×
2
3
1
×
3
7
1
=
5106
2^1 × 3^1 × 23^1 × 37^1 = 5106
2 1 × 3 1 × 2 3 1 × 3 7 1 = 5106
Through this we see that the LCM of 138 and 37 is 5106.
How to Find the LCM of 138 and 37 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 138 and 37 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 37:
What are the Multiples of 138?
What are the Multiples of 37?
Let’s take a look at the first 10 multiples for each of these numbers, 138 and 37:
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
First 10 Multiples of 37: 37, 74, 111, 148, 185, 222, 259, 296, 333, 370
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 37 are 5106, 10212, 15318. Because 5106 is the smallest, it is the least common multiple.
The LCM of 138 and 37 is 5106.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 137 and 91?
What is the LCM of 115 and 8?
What is the LCM of 28 and 16?
What is the LCM of 84 and 98?
What is the LCM of 50 and 17?