Solution: The LCM of 27 and 150 is 1350
Methods
How to find the LCM of 27 and 150 using Prime Factorization
One way to find the LCM of 27 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 27?
What are the Factors of 150?
Here is the prime factorization of 27:
3
3
3^3
3 3
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: 3, 2, 5
2
1
×
3
3
×
5
2
=
1350
2^1 × 3^3 × 5^2 = 1350
2 1 × 3 3 × 5 2 = 1350
Through this we see that the LCM of 27 and 150 is 1350.
How to Find the LCM of 27 and 150 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 27 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, 27 and 150:
What are the Multiples of 27?
What are the Multiples of 150?
Let’s take a look at the first 10 multiples for each of these numbers, 27 and 150:
First 10 Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270
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 27 and 150 are 1350, 2700, 4050. Because 1350 is the smallest, it is the least common multiple.
The LCM of 27 and 150 is 1350.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 80 and 141?
What is the LCM of 127 and 29?
What is the LCM of 64 and 73?
What is the LCM of 103 and 56?
What is the LCM of 91 and 85?