Solution: The LCM of 40 and 109 is 4360
Methods
How to find the LCM of 40 and 109 using Prime Factorization
One way to find the LCM of 40 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 40?
What are the Factors of 109?
Here is the prime factorization of 40:
2
3
×
5
1
2^3 × 5^1
2 3 × 5 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, 5, 109
2
3
×
5
1
×
10
9
1
=
4360
2^3 × 5^1 × 109^1 = 4360
2 3 × 5 1 × 10 9 1 = 4360
Through this we see that the LCM of 40 and 109 is 4360.
How to Find the LCM of 40 and 109 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 40 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, 40 and 109:
What are the Multiples of 40?
What are the Multiples of 109?
Let’s take a look at the first 10 multiples for each of these numbers, 40 and 109:
First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400
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 40 and 109 are 4360, 8720, 13080. Because 4360 is the smallest, it is the least common multiple.
The LCM of 40 and 109 is 4360.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 128 and 19?
What is the LCM of 18 and 50?
What is the LCM of 56 and 49?
What is the LCM of 141 and 24?
What is the LCM of 38 and 140?