Solution: The LCM of 89 and 48 is 4272
Methods
How to find the LCM of 89 and 48 using Prime Factorization
One way to find the LCM of 89 and 48 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 89?
What are the Factors of 48?
Here is the prime factorization of 89:
8
9
1
89^1
8 9 1
And this is the prime factorization of 48:
2
4
×
3
1
2^4 × 3^1
2 4 × 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: 89, 2, 3
2
4
×
3
1
×
8
9
1
=
4272
2^4 × 3^1 × 89^1 = 4272
2 4 × 3 1 × 8 9 1 = 4272
Through this we see that the LCM of 89 and 48 is 4272.
How to Find the LCM of 89 and 48 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 89 and 48 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, 89 and 48:
What are the Multiples of 89?
What are the Multiples of 48?
Let’s take a look at the first 10 multiples for each of these numbers, 89 and 48:
First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890
First 10 Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, 480
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 89 and 48 are 4272, 8544, 12816. Because 4272 is the smallest, it is the least common multiple.
The LCM of 89 and 48 is 4272.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 62 and 137?
What is the LCM of 51 and 39?
What is the LCM of 73 and 14?
What is the LCM of 114 and 112?
What is the LCM of 88 and 17?