Solution: The LCM of 102 and 48 is 816
Methods
How to find the LCM of 102 and 48 using Prime Factorization
One way to find the LCM of 102 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 102?
What are the Factors of 48?
Here is the prime factorization of 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 1 × 1 7 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: 2, 3, 17
2
4
×
3
1
×
1
7
1
=
816
2^4 × 3^1 × 17^1 = 816
2 4 × 3 1 × 1 7 1 = 816
Through this we see that the LCM of 102 and 48 is 816.
How to Find the LCM of 102 and 48 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 102 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, 102 and 48:
What are the Multiples of 102?
What are the Multiples of 48?
Let’s take a look at the first 10 multiples for each of these numbers, 102 and 48:
First 10 Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020
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 102 and 48 are 816, 1632, 2448. Because 816 is the smallest, it is the least common multiple.
The LCM of 102 and 48 is 816.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 49 and 116?
What is the LCM of 63 and 37?
What is the LCM of 72 and 30?
What is the LCM of 11 and 93?
What is the LCM of 137 and 120?