Solution: The LCM of 14 and 92 is 644
Methods
How to find the LCM of 14 and 92 using Prime Factorization
One way to find the LCM of 14 and 92 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 14?
What are the Factors of 92?
Here is the prime factorization of 14:
2
1
×
7
1
2^1 × 7^1
2 1 × 7 1
And this is the prime factorization of 92:
2
2
×
2
3
1
2^2 × 23^1
2 2 × 2 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, 7, 23
2
2
×
7
1
×
2
3
1
=
644
2^2 × 7^1 × 23^1 = 644
2 2 × 7 1 × 2 3 1 = 644
Through this we see that the LCM of 14 and 92 is 644.
How to Find the LCM of 14 and 92 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 14 and 92 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, 14 and 92:
What are the Multiples of 14?
What are the Multiples of 92?
Let’s take a look at the first 10 multiples for each of these numbers, 14 and 92:
First 10 Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140
First 10 Multiples of 92: 92, 184, 276, 368, 460, 552, 644, 736, 828, 920
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 14 and 92 are 644, 1288, 1932. Because 644 is the smallest, it is the least common multiple.
The LCM of 14 and 92 is 644.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 100 and 118?
What is the LCM of 90 and 51?
What is the LCM of 56 and 77?
What is the LCM of 5 and 28?
What is the LCM of 46 and 30?