Solution: The LCM of 51 and 117 is 1989
Methods
How to find the LCM of 51 and 117 using Prime Factorization
One way to find the LCM of 51 and 117 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 51?
What are the Factors of 117?
Here is the prime factorization of 51:
3
1
×
1
7
1
3^1 × 17^1
3 1 × 1 7 1
And this is the prime factorization of 117:
3
2
×
1
3
1
3^2 × 13^1
3 2 × 1 3 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: 3, 17, 13
3
2
×
1
3
1
×
1
7
1
=
1989
3^2 × 13^1 × 17^1 = 1989
3 2 × 1 3 1 × 1 7 1 = 1989
Through this we see that the LCM of 51 and 117 is 1989.
How to Find the LCM of 51 and 117 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 51 and 117 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, 51 and 117:
What are the Multiples of 51?
What are the Multiples of 117?
Let’s take a look at the first 10 multiples for each of these numbers, 51 and 117:
First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510
First 10 Multiples of 117: 117, 234, 351, 468, 585, 702, 819, 936, 1053, 1170
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 51 and 117 are 1989, 3978, 5967. Because 1989 is the smallest, it is the least common multiple.
The LCM of 51 and 117 is 1989.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 71 and 87?
What is the LCM of 40 and 138?
What is the LCM of 104 and 21?
What is the LCM of 86 and 98?
What is the LCM of 45 and 2?