Solution: The LCM of 102 and 100 is 5100
Methods
How to find the LCM of 102 and 100 using Prime Factorization
One way to find the LCM of 102 and 100 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 102?
What are the Factors of 100?
Here is the prime factorization of 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 1 × 1 7 1
And this is the prime factorization of 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 5 2
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, 3, 17, 5
2
2
×
3
1
×
5
2
×
1
7
1
=
5100
2^2 × 3^1 × 5^2 × 17^1 = 5100
2 2 × 3 1 × 5 2 × 1 7 1 = 5100
Through this we see that the LCM of 102 and 100 is 5100.
How to Find the LCM of 102 and 100 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 102 and 100 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, 102 and 100:
What are the Multiples of 102?
What are the Multiples of 100?
Let’s take a look at the first 10 multiples for each of these numbers, 102 and 100:
First 10 Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020
First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
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 102 and 100 are 5100, 10200, 15300. Because 5100 is the smallest, it is the least common multiple.
The LCM of 102 and 100 is 5100.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 24 and 110?
What is the LCM of 113 and 118?
What is the LCM of 14 and 46?
What is the LCM of 45 and 99?
What is the LCM of 31 and 108?