Solution: The LCM of 50 and 98 is 2450
Methods
How to find the LCM of 50 and 98 using Prime Factorization
One way to find the LCM of 50 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 50?
What are the Factors of 98?
Here is the prime factorization of 50:
2
1
×
5
2
2^1 × 5^2
2 1 × 5 2
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, 5, 7
2
1
×
5
2
×
7
2
=
2450
2^1 × 5^2 × 7^2 = 2450
2 1 × 5 2 × 7 2 = 2450
Through this we see that the LCM of 50 and 98 is 2450.
How to Find the LCM of 50 and 98 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 50 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, 50 and 98:
What are the Multiples of 50?
What are the Multiples of 98?
Let’s take a look at the first 10 multiples for each of these numbers, 50 and 98:
First 10 Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500
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 50 and 98 are 2450, 4900, 7350. Because 2450 is the smallest, it is the least common multiple.
The LCM of 50 and 98 is 2450.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 126 and 18?
What is the LCM of 49 and 145?
What is the LCM of 142 and 113?
What is the LCM of 131 and 121?
What is the LCM of 102 and 65?