Solution: The LCM of 47 and 24 is 1128
Methods
How to find the LCM of 47 and 24 using Prime Factorization
One way to find the LCM of 47 and 24 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 47?
What are the Factors of 24?
Here is the prime factorization of 47:
4
7
1
47^1
4 7 1
And this is the prime factorization of 24:
2
3
×
3
1
2^3 × 3^1
2 3 × 3 1
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: 47, 2, 3
2
3
×
3
1
×
4
7
1
=
1128
2^3 × 3^1 × 47^1 = 1128
2 3 × 3 1 × 4 7 1 = 1128
Through this we see that the LCM of 47 and 24 is 1128.
How to Find the LCM of 47 and 24 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 47 and 24 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, 47 and 24:
What are the Multiples of 47?
What are the Multiples of 24?
Let’s take a look at the first 10 multiples for each of these numbers, 47 and 24:
First 10 Multiples of 47: 47, 94, 141, 188, 235, 282, 329, 376, 423, 470
First 10 Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240
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 47 and 24 are 1128, 2256, 3384. Because 1128 is the smallest, it is the least common multiple.
The LCM of 47 and 24 is 1128.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 86 and 122?
What is the LCM of 99 and 119?
What is the LCM of 3 and 85?
What is the LCM of 102 and 34?
What is the LCM of 22 and 58?