Math Tutor Explains: What is the LCM of 61 and 113?

As your math tutor, I'm here to guide you through this problem! To find the LCM of 61 and 113, 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 61?
• What are the Factors of 113?

Here is the prime factorization of 61:

And this is the prime factorization of 113:

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: 61, 113

Through this we see that the LCM of 61 and 113 is 6893.

The first step to this method of finding the Least Common Multiple of 61 and 113 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, 61 and 113:

What are the Multiples of 61?

What are the Multiples of 113?

Let’s take a look at the first 10 multiples for each of these numbers, 61 and 113:

First 10 Multiples of 61: 61, 122, 183, 244, 305, 366, 427, 488, 549, 610

First 10 Multiples of 113: 113, 226, 339, 452, 565, 678, 791, 904, 1017, 1130

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 61 and 113 are 6893, 13786, 20679. Because 6893 is the smallest, it is the least common multiple.

The LCM of 61 and 113 is 6893.

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

• What is the LCM of 102 and 140?
• What is the LCM of 48 and 24?
• What is the LCM of 112 and 64?
• What is the LCM of 71 and 23?
• What is the LCM of 78 and 45?