Solution: The LCM of 126 and 106 is 6678
Methods
How to find the LCM of 126 and 106 using Prime Factorization
One way to find the LCM of 126 and 106 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 126?
What are the Factors of 106?
Here is the prime factorization of 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 7 1
And this is the prime factorization of 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 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, 7, 53
2
1
×
3
2
×
7
1
×
5
3
1
=
6678
2^1 × 3^2 × 7^1 × 53^1 = 6678
2 1 × 3 2 × 7 1 × 5 3 1 = 6678
Through this we see that the LCM of 126 and 106 is 6678.
How to Find the LCM of 126 and 106 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 126 and 106 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, 126 and 106:
What are the Multiples of 126?
What are the Multiples of 106?
Let’s take a look at the first 10 multiples for each of these numbers, 126 and 106:
First 10 Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260
First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060
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 126 and 106 are 6678, 13356, 20034. Because 6678 is the smallest, it is the least common multiple.
The LCM of 126 and 106 is 6678.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 52 and 23?
What is the LCM of 5 and 117?
What is the LCM of 47 and 21?
What is the LCM of 108 and 26?
What is the LCM of 14 and 143?