Solution: The LCM of 78 and 54 is 702
Methods
How to find the LCM of 78 and 54 using Prime Factorization
One way to find the LCM of 78 and 54 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 54?
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 54:
2
1
×
3
3
2^1 × 3^3
2 1 × 3 3
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 78 and 54 is 702.
How to Find the LCM of 78 and 54 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 78 and 54 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 54:
What are the Multiples of 78?
What are the Multiples of 54?
Let’s take a look at the first 10 multiples for each of these numbers, 78 and 54:
First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780
First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540
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 54 are 702, 1404, 2106. Because 702 is the smallest, it is the least common multiple.
The LCM of 78 and 54 is 702.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 132 and 98?
What is the LCM of 110 and 23?
What is the LCM of 83 and 126?
What is the LCM of 134 and 147?
What is the LCM of 87 and 46?