Solution: The LCM of 123 and 150 is 6150
Methods
How to find the LCM of 123 and 150 using Prime Factorization
One way to find the LCM of 123 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 123?
What are the Factors of 150?
Here is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 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: 3, 41, 2, 5
2
1
×
3
1
×
5
2
×
4
1
1
=
6150
2^1 × 3^1 × 5^2 × 41^1 = 6150
2 1 × 3 1 × 5 2 × 4 1 1 = 6150
Through this we see that the LCM of 123 and 150 is 6150.
How to Find the LCM of 123 and 150 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 123 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, 123 and 150:
What are the Multiples of 123?
What are the Multiples of 150?
Let’s take a look at the first 10 multiples for each of these numbers, 123 and 150:
First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230
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 123 and 150 are 6150, 12300, 18450. Because 6150 is the smallest, it is the least common multiple.
The LCM of 123 and 150 is 6150.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 106 and 110?
What is the LCM of 13 and 20?
What is the LCM of 140 and 5?
What is the LCM of 114 and 33?
What is the LCM of 98 and 69?