What is the LCM of 50 and 90?

One way to find the LCM of 50 and 90 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 50?
• What are the Factors of 90?

Here is the prime factorization of 50:

And this is the prime factorization of 90:

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

Through this we see that the LCM of 50 and 90 is 450.

The first step to this method of finding the Least Common Multiple of 50 and 90 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, 50 and 90:

What are the Multiples of 50?

What are the Multiples of 90?

Let’s take a look at the first 10 multiples for each of these numbers, 50 and 90:

First 10 Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500

First 10 Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900

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 50 and 90 are 450, 900, 1350. Because 450 is the smallest, it is the least common multiple.

The LCM of 50 and 90 is 450.

Want more practice? Try some of these other LCM problems:

• What is the LCM of 47 and 8?
• What is the LCM of 150 and 93?
• What is the LCM of 37 and 20?
• What is the LCM of 52 and 45?
• What is the LCM of 5 and 28?