Solution: The LCM of 86 and 150 is 6450
Methods
How to find the LCM of 86 and 150 using Prime Factorization
One way to find the LCM of 86 and 150 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 86?
What are the Factors of 150?
Here is the prime factorization of 86:
2
1
×
4
3
1
2^1 × 43^1
2 1 × 4 3 1
And this is the prime factorization of 150:
2
1
×
3
1
×
5
2
2^1 × 3^1 × 5^2
2 1 × 3 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, 43, 3, 5
2
1
×
3
1
×
5
2
×
4
3
1
=
6450
2^1 × 3^1 × 5^2 × 43^1 = 6450
2 1 × 3 1 × 5 2 × 4 3 1 = 6450
Through this we see that the LCM of 86 and 150 is 6450.
How to Find the LCM of 86 and 150 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 86 and 150 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, 86 and 150:
What are the Multiples of 86?
What are the Multiples of 150?
Let’s take a look at the first 10 multiples for each of these numbers, 86 and 150:
First 10 Multiples of 86: 86, 172, 258, 344, 430, 516, 602, 688, 774, 860
First 10 Multiples of 150: 150, 300, 450, 600, 750, 900, 1050, 1200, 1350, 1500
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 86 and 150 are 6450, 12900, 19350. Because 6450 is the smallest, it is the least common multiple.
The LCM of 86 and 150 is 6450.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 142 and 7?
What is the LCM of 33 and 112?
What is the LCM of 114 and 71?
What is the LCM of 116 and 25?
What is the LCM of 29 and 6?