Solution: The LCM of 90 and 100 is 900
Methods
How to find the LCM of 90 and 100 using Prime Factorization
One way to find the LCM of 90 and 100 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 90?
What are the Factors of 100?
Here is the prime factorization of 90:
2
1
×
3
2
×
5
1
2^1 × 3^2 × 5^1
2 1 × 3 2 × 5 1
And this is the prime factorization of 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 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: 2, 3, 5
2
2
×
3
2
×
5
2
=
900
2^2 × 3^2 × 5^2 = 900
2 2 × 3 2 × 5 2 = 900
Through this we see that the LCM of 90 and 100 is 900.
How to Find the LCM of 90 and 100 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 90 and 100 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, 90 and 100:
What are the Multiples of 90?
What are the Multiples of 100?
Let’s take a look at the first 10 multiples for each of these numbers, 90 and 100:
First 10 Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900
First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
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 90 and 100 are 900, 1800, 2700. Because 900 is the smallest, it is the least common multiple.
The LCM of 90 and 100 is 900.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 62 and 41?
What is the LCM of 138 and 112?
What is the LCM of 18 and 125?
What is the LCM of 52 and 27?
What is the LCM of 70 and 34?