Solution: The LCM of 46 and 50 is 1150
Methods
How to find the LCM of 46 and 50 using Prime Factorization
One way to find the LCM of 46 and 50 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 46?
What are the Factors of 50?
Here is the prime factorization of 46:
2
1
×
2
3
1
2^1 × 23^1
2 1 × 2 3 1
And this is the prime factorization of 50:
2
1
×
5
2
2^1 × 5^2
2 1 × 5 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, 23, 5
2
1
×
5
2
×
2
3
1
=
1150
2^1 × 5^2 × 23^1 = 1150
2 1 × 5 2 × 2 3 1 = 1150
Through this we see that the LCM of 46 and 50 is 1150.
How to Find the LCM of 46 and 50 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 46 and 50 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, 46 and 50:
What are the Multiples of 46?
What are the Multiples of 50?
Let’s take a look at the first 10 multiples for each of these numbers, 46 and 50:
First 10 Multiples of 46: 46, 92, 138, 184, 230, 276, 322, 368, 414, 460
First 10 Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500
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 46 and 50 are 1150, 2300, 3450. Because 1150 is the smallest, it is the least common multiple.
The LCM of 46 and 50 is 1150.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 131 and 147?
What is the LCM of 65 and 83?
What is the LCM of 129 and 13?
What is the LCM of 112 and 23?
What is the LCM of 142 and 1?