Solution: The LCM of 21 and 50 is 1050
Methods
How to find the LCM of 21 and 50 using Prime Factorization
One way to find the LCM of 21 and 50 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 21?
What are the Factors of 50?
Here is the prime factorization of 21:
3
1
×
7
1
3^1 × 7^1
3 1 × 7 1
And this is the prime factorization of 50:
2
1
×
5
2
2^1 × 5^2
2 1 × 5 2
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: 3, 7, 2, 5
2
1
×
3
1
×
5
2
×
7
1
=
1050
2^1 × 3^1 × 5^2 × 7^1 = 1050
2 1 × 3 1 × 5 2 × 7 1 = 1050
Through this we see that the LCM of 21 and 50 is 1050.
How to Find the LCM of 21 and 50 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 21 and 50 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, 21 and 50:
What are the Multiples of 21?
What are the Multiples of 50?
Let’s take a look at the first 10 multiples for each of these numbers, 21 and 50:
First 10 Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210
First 10 Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500
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 21 and 50 are 1050, 2100, 3150. Because 1050 is the smallest, it is the least common multiple.
The LCM of 21 and 50 is 1050.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 87 and 126?
What is the LCM of 63 and 88?
What is the LCM of 80 and 47?
What is the LCM of 40 and 11?
What is the LCM of 56 and 35?