Solution: The LCM of 131 and 78 is 10218
Methods
How to find the LCM of 131 and 78 using Prime Factorization
One way to find the LCM of 131 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 131?
What are the Factors of 78?
Here is the prime factorization of 131:
13
1
1
131^1
13 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: 131, 2, 3, 13
2
1
×
3
1
×
1
3
1
×
13
1
1
=
10218
2^1 × 3^1 × 13^1 × 131^1 = 10218
2 1 × 3 1 × 1 3 1 × 13 1 1 = 10218
Through this we see that the LCM of 131 and 78 is 10218.
How to Find the LCM of 131 and 78 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 131 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, 131 and 78:
What are the Multiples of 131?
What are the Multiples of 78?
Let’s take a look at the first 10 multiples for each of these numbers, 131 and 78:
First 10 Multiples of 131: 131, 262, 393, 524, 655, 786, 917, 1048, 1179, 1310
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 131 and 78 are 10218, 20436, 30654. Because 10218 is the smallest, it is the least common multiple.
The LCM of 131 and 78 is 10218.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 27 and 111?
What is the LCM of 33 and 104?
What is the LCM of 113 and 26?
What is the LCM of 88 and 15?
What is the LCM of 146 and 149?