Solution: The LCM of 93 and 78 is 2418
Methods
How to find the LCM of 93 and 78 using Prime Factorization
One way to find the LCM of 93 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 93?
What are the Factors of 78?
Here is the prime factorization of 93:
3
1
×
3
1
1
3^1 × 31^1
3 1 × 3 1 1
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: 3, 31, 2, 13
2
1
×
3
1
×
1
3
1
×
3
1
1
=
2418
2^1 × 3^1 × 13^1 × 31^1 = 2418
2 1 × 3 1 × 1 3 1 × 3 1 1 = 2418
Through this we see that the LCM of 93 and 78 is 2418.
How to Find the LCM of 93 and 78 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 93 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, 93 and 78:
What are the Multiples of 93?
What are the Multiples of 78?
Let’s take a look at the first 10 multiples for each of these numbers, 93 and 78:
First 10 Multiples of 93: 93, 186, 279, 372, 465, 558, 651, 744, 837, 930
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 93 and 78 are 2418, 4836, 7254. Because 2418 is the smallest, it is the least common multiple.
The LCM of 93 and 78 is 2418.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 27 and 63?
What is the LCM of 43 and 111?
What is the LCM of 118 and 142?
What is the LCM of 10 and 2?
What is the LCM of 41 and 136?