Solution: The LCM of 24 and 30 is 120
Methods
How to find the LCM of 24 and 30 using Prime Factorization
One way to find the LCM of 24 and 30 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 24?
What are the Factors of 30?
Here is the prime factorization of 24:
2
3
×
3
1
2^3 × 3^1
2 3 × 3 1
And this is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 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, 5
2
3
×
3
1
×
5
1
=
120
2^3 × 3^1 × 5^1 = 120
2 3 × 3 1 × 5 1 = 120
Through this we see that the LCM of 24 and 30 is 120.
How to Find the LCM of 24 and 30 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 24 and 30 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, 24 and 30:
What are the Multiples of 24?
What are the Multiples of 30?
Let’s take a look at the first 10 multiples for each of these numbers, 24 and 30:
First 10 Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
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 24 and 30 are 120, 240, 360. Because 120 is the smallest, it is the least common multiple.
The LCM of 24 and 30 is 120.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 118 and 58?
What is the LCM of 69 and 92?
What is the LCM of 12 and 141?
What is the LCM of 35 and 55?
What is the LCM of 77 and 126?