Solution: The LCM of 51 and 125 is 6375
Methods
How to find the LCM of 51 and 125 using Prime Factorization
One way to find the LCM of 51 and 125 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 125?
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 125:
5
3
5^3
5 3
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, 5
3
1
×
5
3
×
1
7
1
=
6375
3^1 × 5^3 × 17^1 = 6375
3 1 × 5 3 × 1 7 1 = 6375
Through this we see that the LCM of 51 and 125 is 6375.
How to Find the LCM of 51 and 125 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 51 and 125 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 125:
What are the Multiples of 51?
What are the Multiples of 125?
Let’s take a look at the first 10 multiples for each of these numbers, 51 and 125:
First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510
First 10 Multiples of 125: 125, 250, 375, 500, 625, 750, 875, 1000, 1125, 1250
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 125 are 6375, 12750, 19125. Because 6375 is the smallest, it is the least common multiple.
The LCM of 51 and 125 is 6375.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 41 and 47?
What is the LCM of 48 and 90?
What is the LCM of 109 and 57?
What is the LCM of 136 and 50?
What is the LCM of 76 and 95?