Solution: The LCM of 109 and 123 is 13407
Methods
How to find the LCM of 109 and 123 using Prime Factorization
One way to find the LCM of 109 and 123 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 109?
What are the Factors of 123?
Here is the prime factorization of 109:
10
9
1
109^1
10 9 1
And this is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 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: 109, 3, 41
3
1
×
4
1
1
×
10
9
1
=
13407
3^1 × 41^1 × 109^1 = 13407
3 1 × 4 1 1 × 10 9 1 = 13407
Through this we see that the LCM of 109 and 123 is 13407.
How to Find the LCM of 109 and 123 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 109 and 123 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, 109 and 123:
What are the Multiples of 109?
What are the Multiples of 123?
Let’s take a look at the first 10 multiples for each of these numbers, 109 and 123:
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230
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 109 and 123 are 13407, 26814, 40221. Because 13407 is the smallest, it is the least common multiple.
The LCM of 109 and 123 is 13407.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 130 and 26?
What is the LCM of 28 and 10?
What is the LCM of 74 and 67?
What is the LCM of 54 and 94?
What is the LCM of 103 and 99?