Solution: The LCM of 12 and 26 is 156
Methods
How to find the LCM of 12 and 26 using Prime Factorization
One way to find the LCM of 12 and 26 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 12?
What are the Factors of 26?
Here is the prime factorization of 12:
2
2
×
3
1
2^2 × 3^1
2 2 × 3 1
And this is the prime factorization of 26:
2
1
×
1
3
1
2^1 × 13^1
2 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
2
×
3
1
×
1
3
1
=
156
2^2 × 3^1 × 13^1 = 156
2 2 × 3 1 × 1 3 1 = 156
Through this we see that the LCM of 12 and 26 is 156.
How to Find the LCM of 12 and 26 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 12 and 26 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, 12 and 26:
What are the Multiples of 12?
What are the Multiples of 26?
Let’s take a look at the first 10 multiples for each of these numbers, 12 and 26:
First 10 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
First 10 Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260
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 12 and 26 are 156, 312, 468. Because 156 is the smallest, it is the least common multiple.
The LCM of 12 and 26 is 156.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 140 and 30?
What is the LCM of 136 and 86?
What is the LCM of 146 and 109?
What is the LCM of 43 and 122?
What is the LCM of 133 and 127?