What is the LCM of 123 and 6?

One way to find the LCM of 123 and 6 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 6?

Here is the prime factorization of 123:

And this is the prime factorization of 6:

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

Through this we see that the LCM of 123 and 6 is 246.

The first step to this method of finding the Least Common Multiple of 123 and 6 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 6:

What are the Multiples of 123?

What are the Multiples of 6?

Let’s take a look at the first 10 multiples for each of these numbers, 123 and 6:

First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230

First 10 Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

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 6 are 246, 492, 738. Because 246 is the smallest, it is the least common multiple.

The LCM of 123 and 6 is 246.

Want more practice? Try some of these other LCM problems:

• What is the LCM of 46 and 84?
• What is the LCM of 69 and 2?
• What is the LCM of 31 and 73?
• What is the LCM of 59 and 132?
• What is the LCM of 99 and 136?