Solution: The LCM of 109 and 43 is 4687
Methods
How to find the LCM of 109 and 43 using Prime Factorization
One way to find the LCM of 109 and 43 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 43?
Here is the prime factorization of 109:
10
9
1
109^1
10 9 1
And this is the prime factorization of 43:
4
3
1
43^1
4 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: 109, 43
4
3
1
×
10
9
1
=
4687
43^1 × 109^1 = 4687
4 3 1 × 10 9 1 = 4687
Through this we see that the LCM of 109 and 43 is 4687.
How to Find the LCM of 109 and 43 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 109 and 43 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 43:
What are the Multiples of 109?
What are the Multiples of 43?
Let’s take a look at the first 10 multiples for each of these numbers, 109 and 43:
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
First 10 Multiples of 43: 43, 86, 129, 172, 215, 258, 301, 344, 387, 430
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 43 are 4687, 9374, 14061. Because 4687 is the smallest, it is the least common multiple.
The LCM of 109 and 43 is 4687.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 144 and 114?
What is the LCM of 31 and 83?
What is the LCM of 127 and 22?
What is the LCM of 53 and 122?
What is the LCM of 100 and 75?