Solution: The LCM of 120 and 98 is 5880
Methods
How to find the LCM of 120 and 98 using Prime Factorization
One way to find the LCM of 120 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 120?
What are the Factors of 98?
Here is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 5 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, 5, 7
2
3
×
3
1
×
5
1
×
7
2
=
5880
2^3 × 3^1 × 5^1 × 7^2 = 5880
2 3 × 3 1 × 5 1 × 7 2 = 5880
Through this we see that the LCM of 120 and 98 is 5880.
How to Find the LCM of 120 and 98 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 120 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, 120 and 98:
What are the Multiples of 120?
What are the Multiples of 98?
Let’s take a look at the first 10 multiples for each of these numbers, 120 and 98:
First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200
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 120 and 98 are 5880, 11760, 17640. Because 5880 is the smallest, it is the least common multiple.
The LCM of 120 and 98 is 5880.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 88 and 126?
What is the LCM of 9 and 106?
What is the LCM of 82 and 139?
What is the LCM of 22 and 39?
What is the LCM of 93 and 67?