Solution: The LCM of 102 and 98 is 4998
Methods
How to find the LCM of 102 and 98 using Prime Factorization
One way to find the LCM of 102 and 98 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 98?
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 98:
2
1
×
7
2
2^1 × 7^2
2 1 × 7 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, 7
2
1
×
3
1
×
7
2
×
1
7
1
=
4998
2^1 × 3^1 × 7^2 × 17^1 = 4998
2 1 × 3 1 × 7 2 × 1 7 1 = 4998
Through this we see that the LCM of 102 and 98 is 4998.
How to Find the LCM of 102 and 98 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 102 and 98 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 98:
What are the Multiples of 102?
What are the Multiples of 98?
Let’s take a look at the first 10 multiples for each of these numbers, 102 and 98:
First 10 Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020
First 10 Multiples of 98: 98, 196, 294, 392, 490, 588, 686, 784, 882, 980
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 98 are 4998, 9996, 14994. Because 4998 is the smallest, it is the least common multiple.
The LCM of 102 and 98 is 4998.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 56 and 86?
What is the LCM of 68 and 24?
What is the LCM of 149 and 74?
What is the LCM of 7 and 21?
What is the LCM of 15 and 59?