Solution: The LCM of 48 and 138 is 1104
Methods
How to find the LCM of 48 and 138 using Prime Factorization
One way to find the LCM of 48 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 48?
What are the Factors of 138?
Here is the prime factorization of 48:
2
4
×
3
1
2^4 × 3^1
2 4 × 3 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: 2, 3, 23
2
4
×
3
1
×
2
3
1
=
1104
2^4 × 3^1 × 23^1 = 1104
2 4 × 3 1 × 2 3 1 = 1104
Through this we see that the LCM of 48 and 138 is 1104.
How to Find the LCM of 48 and 138 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 48 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, 48 and 138:
What are the Multiples of 48?
What are the Multiples of 138?
Let’s take a look at the first 10 multiples for each of these numbers, 48 and 138:
First 10 Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, 480
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 48 and 138 are 1104, 2208, 3312. Because 1104 is the smallest, it is the least common multiple.
The LCM of 48 and 138 is 1104.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 134 and 147?
What is the LCM of 53 and 136?
What is the LCM of 70 and 138?
What is the LCM of 150 and 57?
What is the LCM of 72 and 107?