Solution: The LCM of 104 and 48 is 624
Methods
How to find the LCM of 104 and 48 using Prime Factorization
One way to find the LCM of 104 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 104?
What are the Factors of 48?
Here is the prime factorization of 104:
2
3
×
1
3
1
2^3 × 13^1
2 3 × 1 3 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, 13, 3
2
4
×
3
1
×
1
3
1
=
624
2^4 × 3^1 × 13^1 = 624
2 4 × 3 1 × 1 3 1 = 624
Through this we see that the LCM of 104 and 48 is 624.
How to Find the LCM of 104 and 48 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 104 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, 104 and 48:
What are the Multiples of 104?
What are the Multiples of 48?
Let’s take a look at the first 10 multiples for each of these numbers, 104 and 48:
First 10 Multiples of 104: 104, 208, 312, 416, 520, 624, 728, 832, 936, 1040
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 104 and 48 are 624, 1248, 1872. Because 624 is the smallest, it is the least common multiple.
The LCM of 104 and 48 is 624.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 77 and 71?
What is the LCM of 39 and 95?
What is the LCM of 81 and 139?
What is the LCM of 55 and 38?
What is the LCM of 142 and 27?