Math Tutor Explains: What is the LCM of 24 and 101?

As your math tutor, I'm here to guide you through this problem! To find the LCM of 24 and 101, 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 24?
• What are the Factors of 101?

Here is the prime factorization of 24:

And this is the prime factorization of 101:

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: 2, 3, 101

Through this we see that the LCM of 24 and 101 is 2424.

The first step to this method of finding the Least Common Multiple of 24 and 101 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, 24 and 101:

What are the Multiples of 24?

What are the Multiples of 101?

Let’s take a look at the first 10 multiples for each of these numbers, 24 and 101:

First 10 Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240

First 10 Multiples of 101: 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010

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 24 and 101 are 2424, 4848, 7272. Because 2424 is the smallest, it is the least common multiple.

The LCM of 24 and 101 is 2424.

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

• What is the LCM of 105 and 140?
• What is the LCM of 34 and 6?
• What is the LCM of 14 and 77?
• What is the LCM of 58 and 117?
• What is the LCM of 131 and 65?