Solution: The LCM of 80 and 48 is 240
Methods
How to find the LCM of 80 and 48 using Prime Factorization
One way to find the LCM of 80 and 48 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 80?
What are the Factors of 48?
Here is the prime factorization of 80:
2
4
×
5
1
2^4 × 5^1
2 4 × 5 1
And this is the prime factorization of 48:
2
4
×
3
1
2^4 × 3^1
2 4 × 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, 5, 3
2
4
×
3
1
×
5
1
=
240
2^4 × 3^1 × 5^1 = 240
2 4 × 3 1 × 5 1 = 240
Through this we see that the LCM of 80 and 48 is 240.
How to Find the LCM of 80 and 48 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 80 and 48 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, 80 and 48:
What are the Multiples of 80?
What are the Multiples of 48?
Let’s take a look at the first 10 multiples for each of these numbers, 80 and 48:
First 10 Multiples of 80: 80, 160, 240, 320, 400, 480, 560, 640, 720, 800
First 10 Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, 480
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 80 and 48 are 240, 480, 720. Because 240 is the smallest, it is the least common multiple.
The LCM of 80 and 48 is 240.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 128 and 43?
What is the LCM of 127 and 30?
What is the LCM of 2 and 13?
What is the LCM of 65 and 12?
What is the LCM of 124 and 125?