What is the LCM of 33 and 123?

One way to find the LCM of 33 and 123 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 33?
• What are the Factors of 123?

Here is the prime factorization of 33:

And this is the prime factorization of 123:

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, 11, 41

Through this we see that the LCM of 33 and 123 is 1353.

The first step to this method of finding the Least Common Multiple of 33 and 123 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, 33 and 123:

What are the Multiples of 33?

What are the Multiples of 123?

Let’s take a look at the first 10 multiples for each of these numbers, 33 and 123:

First 10 Multiples of 33: 33, 66, 99, 132, 165, 198, 231, 264, 297, 330

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

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 33 and 123 are 1353, 2706, 4059. Because 1353 is the smallest, it is the least common multiple.

The LCM of 33 and 123 is 1353.

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

• What is the LCM of 3 and 146?
• What is the LCM of 5 and 4?
• What is the LCM of 103 and 42?
• What is the LCM of 111 and 59?
• What is the LCM of 130 and 6?