Solution: The LCM of 125 and 46 is 5750
Methods
How to find the LCM of 125 and 46 using Prime Factorization
One way to find the LCM of 125 and 46 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 125?
What are the Factors of 46?
Here is the prime factorization of 125:
5
3
5^3
5 3
And this is the prime factorization of 46:
2
1
×
2
3
1
2^1 × 23^1
2 1 × 2 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: 5, 2, 23
2
1
×
5
3
×
2
3
1
=
5750
2^1 × 5^3 × 23^1 = 5750
2 1 × 5 3 × 2 3 1 = 5750
Through this we see that the LCM of 125 and 46 is 5750.
How to Find the LCM of 125 and 46 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 125 and 46 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, 125 and 46:
What are the Multiples of 125?
What are the Multiples of 46?
Let’s take a look at the first 10 multiples for each of these numbers, 125 and 46:
First 10 Multiples of 125: 125, 250, 375, 500, 625, 750, 875, 1000, 1125, 1250
First 10 Multiples of 46: 46, 92, 138, 184, 230, 276, 322, 368, 414, 460
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 125 and 46 are 5750, 11500, 17250. Because 5750 is the smallest, it is the least common multiple.
The LCM of 125 and 46 is 5750.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 18 and 109?
What is the LCM of 100 and 13?
What is the LCM of 68 and 92?
What is the LCM of 84 and 80?
What is the LCM of 9 and 88?