Solution: The LCM of 138 and 60 is 1380
Methods
How to find the LCM of 138 and 60 using Prime Factorization
One way to find the LCM of 138 and 60 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 60?
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 60:
2
2
×
3
1
×
5
1
2^2 × 3^1 × 5^1
2 2 × 3 1 × 5 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, 5
2
2
×
3
1
×
5
1
×
2
3
1
=
1380
2^2 × 3^1 × 5^1 × 23^1 = 1380
2 2 × 3 1 × 5 1 × 2 3 1 = 1380
Through this we see that the LCM of 138 and 60 is 1380.
How to Find the LCM of 138 and 60 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 138 and 60 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 60:
What are the Multiples of 138?
What are the Multiples of 60?
Let’s take a look at the first 10 multiples for each of these numbers, 138 and 60:
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
First 10 Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600
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 60 are 1380, 2760, 4140. Because 1380 is the smallest, it is the least common multiple.
The LCM of 138 and 60 is 1380.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 45 and 54?
What is the LCM of 112 and 87?
What is the LCM of 136 and 148?
What is the LCM of 68 and 74?
What is the LCM of 59 and 70?