Solution: The LCM of 100 and 105 is 2100
Methods
How to find the LCM of 100 and 105 using Prime Factorization
One way to find the LCM of 100 and 105 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 105?
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 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 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, 5, 3, 7
2
2
×
3
1
×
5
2
×
7
1
=
2100
2^2 × 3^1 × 5^2 × 7^1 = 2100
2 2 × 3 1 × 5 2 × 7 1 = 2100
Through this we see that the LCM of 100 and 105 is 2100.
How to Find the LCM of 100 and 105 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 100 and 105 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 105:
What are the Multiples of 100?
What are the Multiples of 105?
Let’s take a look at the first 10 multiples for each of these numbers, 100 and 105:
First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050
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 105 are 2100, 4200, 6300. Because 2100 is the smallest, it is the least common multiple.
The LCM of 100 and 105 is 2100.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 5 and 139?
What is the LCM of 118 and 32?
What is the LCM of 37 and 45?
What is the LCM of 135 and 89?
What is the LCM of 108 and 130?