Solution: The LCM of 78 and 32 is 1248
Methods
How to find the LCM of 78 and 32 using Prime Factorization
One way to find the LCM of 78 and 32 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 78?
What are the Factors of 32?
Here is the prime factorization of 78:
2
1
×
3
1
×
1
3
1
2^1 × 3^1 × 13^1
2 1 × 3 1 × 1 3 1
And this is the prime factorization of 32:
2
5
2^5
2 5
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, 13
2
5
×
3
1
×
1
3
1
=
1248
2^5 × 3^1 × 13^1 = 1248
2 5 × 3 1 × 1 3 1 = 1248
Through this we see that the LCM of 78 and 32 is 1248.
How to Find the LCM of 78 and 32 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 78 and 32 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, 78 and 32:
What are the Multiples of 78?
What are the Multiples of 32?
Let’s take a look at the first 10 multiples for each of these numbers, 78 and 32:
First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780
First 10 Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320
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 78 and 32 are 1248, 2496, 3744. Because 1248 is the smallest, it is the least common multiple.
The LCM of 78 and 32 is 1248.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 5 and 52?
What is the LCM of 131 and 67?
What is the LCM of 65 and 70?
What is the LCM of 1 and 113?
What is the LCM of 61 and 73?