Solution: The LCM of 56 and 98 is 392
Methods
How to find the LCM of 56 and 98 using Prime Factorization
One way to find the LCM of 56 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 56?
What are the Factors of 98?
Here is the prime factorization of 56:
2
3
×
7
1
2^3 × 7^1
2 3 × 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, 7
2
3
×
7
2
=
392
2^3 × 7^2 = 392
2 3 × 7 2 = 392
Through this we see that the LCM of 56 and 98 is 392.
How to Find the LCM of 56 and 98 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 56 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, 56 and 98:
What are the Multiples of 56?
What are the Multiples of 98?
Let’s take a look at the first 10 multiples for each of these numbers, 56 and 98:
First 10 Multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448, 504, 560
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 56 and 98 are 392, 784, 1176. Because 392 is the smallest, it is the least common multiple.
The LCM of 56 and 98 is 392.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 122 and 132?
What is the LCM of 57 and 62?
What is the LCM of 125 and 92?
What is the LCM of 33 and 69?
What is the LCM of 3 and 86?