Solution: The LCM of 100 and 12 is 300
Methods
How to find the LCM of 100 and 12 using Prime Factorization
One way to find the LCM of 100 and 12 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 100?
What are the Factors of 12?
Here is the prime factorization of 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 5 2
And this is the prime factorization of 12:
2
2
×
3
1
2^2 × 3^1
2 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: 2, 5, 3
2
2
×
3
1
×
5
2
=
300
2^2 × 3^1 × 5^2 = 300
2 2 × 3 1 × 5 2 = 300
Through this we see that the LCM of 100 and 12 is 300.
How to Find the LCM of 100 and 12 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 100 and 12 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, 100 and 12:
What are the Multiples of 100?
What are the Multiples of 12?
Let’s take a look at the first 10 multiples for each of these numbers, 100 and 12:
First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
First 10 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
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 100 and 12 are 300, 600, 900. Because 300 is the smallest, it is the least common multiple.
The LCM of 100 and 12 is 300.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 67 and 101?
What is the LCM of 6 and 35?
What is the LCM of 54 and 132?
What is the LCM of 81 and 88?
What is the LCM of 116 and 3?