Solution: The LCM of 98 and 36 is 1764
Methods
How to find the LCM of 98 and 36 using Prime Factorization
One way to find the LCM of 98 and 36 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 36?
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 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 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, 3
2
2
×
3
2
×
7
2
=
1764
2^2 × 3^2 × 7^2 = 1764
2 2 × 3 2 × 7 2 = 1764
Through this we see that the LCM of 98 and 36 is 1764.
How to Find the LCM of 98 and 36 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 98 and 36 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 36:
What are the Multiples of 98?
What are the Multiples of 36?
Let’s take a look at the first 10 multiples for each of these numbers, 98 and 36:
First 10 Multiples of 98: 98, 196, 294, 392, 490, 588, 686, 784, 882, 980
First 10 Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360
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 36 are 1764, 3528, 5292. Because 1764 is the smallest, it is the least common multiple.
The LCM of 98 and 36 is 1764.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 70 and 43?
What is the LCM of 49 and 103?
What is the LCM of 9 and 81?
What is the LCM of 4 and 76?
What is the LCM of 17 and 114?