Solution: The LCM of 104 and 147 is 15288
Methods
How to find the LCM of 104 and 147 using Prime Factorization
One way to find the LCM of 104 and 147 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 147?
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 147:
3
1
×
7
2
3^1 × 7^2
3 1 × 7 2
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, 7
2
3
×
3
1
×
7
2
×
1
3
1
=
15288
2^3 × 3^1 × 7^2 × 13^1 = 15288
2 3 × 3 1 × 7 2 × 1 3 1 = 15288
Through this we see that the LCM of 104 and 147 is 15288.
How to Find the LCM of 104 and 147 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 104 and 147 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 147:
What are the Multiples of 104?
What are the Multiples of 147?
Let’s take a look at the first 10 multiples for each of these numbers, 104 and 147:
First 10 Multiples of 104: 104, 208, 312, 416, 520, 624, 728, 832, 936, 1040
First 10 Multiples of 147: 147, 294, 441, 588, 735, 882, 1029, 1176, 1323, 1470
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 147 are 15288, 30576, 45864. Because 15288 is the smallest, it is the least common multiple.
The LCM of 104 and 147 is 15288.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 127 and 150?
What is the LCM of 78 and 71?
What is the LCM of 55 and 46?
What is the LCM of 144 and 56?
What is the LCM of 79 and 75?