Math Tutor Explains: What is the LCM of 49 and 64?

As your math tutor, I'm here to guide you through this problem! To find the LCM of 49 and 64, 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 49?
• What are the Factors of 64?

Here is the prime factorization of 49:

And this is the prime factorization of 64:

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: 7, 2

Through this we see that the LCM of 49 and 64 is 3136.

The first step to this method of finding the Least Common Multiple of 49 and 64 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, 49 and 64:

What are the Multiples of 49?

What are the Multiples of 64?

Let’s take a look at the first 10 multiples for each of these numbers, 49 and 64:

First 10 Multiples of 49: 49, 98, 147, 196, 245, 294, 343, 392, 441, 490

First 10 Multiples of 64: 64, 128, 192, 256, 320, 384, 448, 512, 576, 640

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 49 and 64 are 3136, 6272, 9408. Because 3136 is the smallest, it is the least common multiple.

The LCM of 49 and 64 is 3136.

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

• What is the LCM of 75 and 61?
• What is the LCM of 111 and 8?
• What is the LCM of 80 and 65?
• What is the LCM of 116 and 81?
• What is the LCM of 47 and 31?