Solution: The LCM of 150 and 84 is 2100
Methods
How to find the LCM of 150 and 84 using Prime Factorization
One way to find the LCM of 150 and 84 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 84?
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 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 7 1
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, 7
2
2
×
3
1
×
5
2
×
7
1
=
2100
2^2 × 3^1 × 5^2 × 7^1 = 2100
2 2 × 3 1 × 5 2 × 7 1 = 2100
Through this we see that the LCM of 150 and 84 is 2100.
How to Find the LCM of 150 and 84 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 150 and 84 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 84:
What are the Multiples of 150?
What are the Multiples of 84?
Let’s take a look at the first 10 multiples for each of these numbers, 150 and 84:
First 10 Multiples of 150: 150, 300, 450, 600, 750, 900, 1050, 1200, 1350, 1500
First 10 Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840
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 84 are 2100, 4200, 6300. Because 2100 is the smallest, it is the least common multiple.
The LCM of 150 and 84 is 2100.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 105 and 41?
What is the LCM of 147 and 2?
What is the LCM of 146 and 140?
What is the LCM of 46 and 47?
What is the LCM of 149 and 87?