Math Tutor Explains: What is the LCM of 63 and 17?

As your math tutor, I'm here to guide you through this problem! To find the LCM of 63 and 17, one effective method is comparing their prime factorizations. Start by breaking each number down into its prime factors. Follow these steps to determine the prime factorization of each number:

• What are the Factors of 63?
• What are the Factors of 17?

Here is the prime factorization of 63:

And this is the prime factorization of 17:

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, 7, 17

Through this we see that the LCM of 63 and 17 is 1071.

The first step to this method of finding the Least Common Multiple of 63 and 17 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, 63 and 17:

What are the Multiples of 63?

What are the Multiples of 17?

Let’s take a look at the first 10 multiples for each of these numbers, 63 and 17:

First 10 Multiples of 63: 63, 126, 189, 252, 315, 378, 441, 504, 567, 630

First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170

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 63 and 17 are 1071, 2142, 3213. Because 1071 is the smallest, it is the least common multiple.

The LCM of 63 and 17 is 1071.

Want more practice? As a math tutor, I encourage you to try some of these other LCM problems:

• What is the LCM of 119 and 36?
• What is the LCM of 78 and 81?
• What is the LCM of 61 and 86?
• What is the LCM of 89 and 135?
• What is the LCM of 54 and 62?