Solution: The LCM of 150 and 72 is 1800
Methods
How to find the LCM of 150 and 72 using Prime Factorization
One way to find the LCM of 150 and 72 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 150?
What are the Factors of 72?
Here is the prime factorization of 150:
2
1
×
3
1
×
5
2
2^1 × 3^1 × 5^2
2 1 × 3 1 × 5 2
And this is the prime factorization of 72:
2
3
×
3
2
2^3 × 3^2
2 3 × 3 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, 3, 5
2
3
×
3
2
×
5
2
=
1800
2^3 × 3^2 × 5^2 = 1800
2 3 × 3 2 × 5 2 = 1800
Through this we see that the LCM of 150 and 72 is 1800.
How to Find the LCM of 150 and 72 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 150 and 72 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, 150 and 72:
What are the Multiples of 150?
What are the Multiples of 72?
Let’s take a look at the first 10 multiples for each of these numbers, 150 and 72:
First 10 Multiples of 150: 150, 300, 450, 600, 750, 900, 1050, 1200, 1350, 1500
First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720
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 150 and 72 are 1800, 3600, 5400. Because 1800 is the smallest, it is the least common multiple.
The LCM of 150 and 72 is 1800.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 66 and 17?
What is the LCM of 55 and 106?
What is the LCM of 4 and 149?
What is the LCM of 36 and 6?
What is the LCM of 61 and 54?