Solution: The LCM of 120 and 51 is 2040
Methods
How to find the LCM of 120 and 51 using Prime Factorization
One way to find the LCM of 120 and 51 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 51?
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 51:
3
1
×
1
7
1
3^1 × 17^1
3 1 × 1 7 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, 17
2
3
×
3
1
×
5
1
×
1
7
1
=
2040
2^3 × 3^1 × 5^1 × 17^1 = 2040
2 3 × 3 1 × 5 1 × 1 7 1 = 2040
Through this we see that the LCM of 120 and 51 is 2040.
How to Find the LCM of 120 and 51 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 120 and 51 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 51:
What are the Multiples of 120?
What are the Multiples of 51?
Let’s take a look at the first 10 multiples for each of these numbers, 120 and 51:
First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200
First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510
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 51 are 2040, 4080, 6120. Because 2040 is the smallest, it is the least common multiple.
The LCM of 120 and 51 is 2040.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 10 and 96?
What is the LCM of 21 and 67?
What is the LCM of 57 and 7?
What is the LCM of 99 and 150?
What is the LCM of 118 and 90?