Solution: The LCM of 98 and 100 is 4900
Methods
How to find the LCM of 98 and 100 using Prime Factorization
One way to find the LCM of 98 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 98?
What are the Factors of 100?
Here is the prime factorization of 98:
2
1
×
7
2
2^1 × 7^2
2 1 × 7 2
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, 7, 5
2
2
×
5
2
×
7
2
=
4900
2^2 × 5^2 × 7^2 = 4900
2 2 × 5 2 × 7 2 = 4900
Through this we see that the LCM of 98 and 100 is 4900.
How to Find the LCM of 98 and 100 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 98 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, 98 and 100:
What are the Multiples of 98?
What are the Multiples of 100?
Let’s take a look at the first 10 multiples for each of these numbers, 98 and 100:
First 10 Multiples of 98: 98, 196, 294, 392, 490, 588, 686, 784, 882, 980
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 98 and 100 are 4900, 9800, 14700. Because 4900 is the smallest, it is the least common multiple.
The LCM of 98 and 100 is 4900.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 136 and 106?
What is the LCM of 119 and 108?
What is the LCM of 128 and 42?
What is the LCM of 104 and 32?
What is the LCM of 76 and 137?