Solution: The LCM of 120 and 33 is 1320
Methods
How to find the LCM of 120 and 33 using Prime Factorization
One way to find the LCM of 120 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 120?
What are the Factors of 33?
Here is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 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
3
×
3
1
×
5
1
×
1
1
1
=
1320
2^3 × 3^1 × 5^1 × 11^1 = 1320
2 3 × 3 1 × 5 1 × 1 1 1 = 1320
Through this we see that the LCM of 120 and 33 is 1320.
How to Find the LCM of 120 and 33 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 120 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, 120 and 33:
What are the Multiples of 120?
What are the Multiples of 33?
Let’s take a look at the first 10 multiples for each of these numbers, 120 and 33:
First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200
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 120 and 33 are 1320, 2640, 3960. Because 1320 is the smallest, it is the least common multiple.
The LCM of 120 and 33 is 1320.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 140 and 54?
What is the LCM of 114 and 146?
What is the LCM of 37 and 91?
What is the LCM of 42 and 150?
What is the LCM of 14 and 12?