Solution: The LCM of 126 and 109 is 13734
Methods
How to find the LCM of 126 and 109 using Prime Factorization
One way to find the LCM of 126 and 109 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 109?
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 109:
10
9
1
109^1
10 9 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, 109
2
1
×
3
2
×
7
1
×
10
9
1
=
13734
2^1 × 3^2 × 7^1 × 109^1 = 13734
2 1 × 3 2 × 7 1 × 10 9 1 = 13734
Through this we see that the LCM of 126 and 109 is 13734.
How to Find the LCM of 126 and 109 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 126 and 109 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 109:
What are the Multiples of 126?
What are the Multiples of 109?
Let’s take a look at the first 10 multiples for each of these numbers, 126 and 109:
First 10 Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
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 109 are 13734, 27468, 41202. Because 13734 is the smallest, it is the least common multiple.
The LCM of 126 and 109 is 13734.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 88 and 78?
What is the LCM of 54 and 64?
What is the LCM of 29 and 70?
What is the LCM of 13 and 129?
What is the LCM of 149 and 145?