Solution: The LCM of 90 and 33 is 990
Methods
How to find the LCM of 90 and 33 using Prime Factorization
One way to find the LCM of 90 and 33 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 33?
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 33:
3
1
×
1
1
1
3^1 × 11^1
3 1 × 1 1 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, 11
2
1
×
3
2
×
5
1
×
1
1
1
=
990
2^1 × 3^2 × 5^1 × 11^1 = 990
2 1 × 3 2 × 5 1 × 1 1 1 = 990
Through this we see that the LCM of 90 and 33 is 990.
How to Find the LCM of 90 and 33 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 90 and 33 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 33:
What are the Multiples of 90?
What are the Multiples of 33?
Let’s take a look at the first 10 multiples for each of these numbers, 90 and 33:
First 10 Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900
First 10 Multiples of 33: 33, 66, 99, 132, 165, 198, 231, 264, 297, 330
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 33 are 990, 1980, 2970. Because 990 is the smallest, it is the least common multiple.
The LCM of 90 and 33 is 990.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 25 and 111?
What is the LCM of 85 and 60?
What is the LCM of 144 and 74?
What is the LCM of 28 and 127?
What is the LCM of 23 and 40?