Solution: The LCM of 54 and 78 is 702
Methods
How to find the LCM of 54 and 78 using Prime Factorization
One way to find the LCM of 54 and 78 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 54?
What are the Factors of 78?
Here is the prime factorization of 54:
2
1
×
3
3
2^1 × 3^3
2 1 × 3 3
And this 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
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
1
×
3
3
×
1
3
1
=
702
2^1 × 3^3 × 13^1 = 702
2 1 × 3 3 × 1 3 1 = 702
Through this we see that the LCM of 54 and 78 is 702.
How to Find the LCM of 54 and 78 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 54 and 78 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, 54 and 78:
What are the Multiples of 54?
What are the Multiples of 78?
Let’s take a look at the first 10 multiples for each of these numbers, 54 and 78:
First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540
First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780
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 54 and 78 are 702, 1404, 2106. Because 702 is the smallest, it is the least common multiple.
The LCM of 54 and 78 is 702.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 91 and 19?
What is the LCM of 125 and 43?
What is the LCM of 46 and 116?
What is the LCM of 102 and 118?
What is the LCM of 82 and 137?