Solution: The LCM of 30 and 21 is 210
Methods
How to find the LCM of 30 and 21 using Prime Factorization
One way to find the LCM of 30 and 21 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 30?
What are the Factors of 21?
Here is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 3 1 × 5 1
And this is the prime factorization of 21:
3
1
×
7
1
3^1 × 7^1
3 1 × 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, 5, 7
2
1
×
3
1
×
5
1
×
7
1
=
210
2^1 × 3^1 × 5^1 × 7^1 = 210
2 1 × 3 1 × 5 1 × 7 1 = 210
Through this we see that the LCM of 30 and 21 is 210.
How to Find the LCM of 30 and 21 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 30 and 21 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, 30 and 21:
What are the Multiples of 30?
What are the Multiples of 21?
Let’s take a look at the first 10 multiples for each of these numbers, 30 and 21:
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
First 10 Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210
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 30 and 21 are 210, 420, 630. Because 210 is the smallest, it is the least common multiple.
The LCM of 30 and 21 is 210.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 100 and 66?
What is the LCM of 140 and 149?
What is the LCM of 120 and 133?
What is the LCM of 127 and 138?
What is the LCM of 9 and 83?