Solution: The LCM of 106 and 40 is 2120
Methods
How to find the LCM of 106 and 40 using Prime Factorization
One way to find the LCM of 106 and 40 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 106?
What are the Factors of 40?
Here is the prime factorization of 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 3 1
And this is the prime factorization of 40:
2
3
×
5
1
2^3 × 5^1
2 3 × 5 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, 53, 5
2
3
×
5
1
×
5
3
1
=
2120
2^3 × 5^1 × 53^1 = 2120
2 3 × 5 1 × 5 3 1 = 2120
Through this we see that the LCM of 106 and 40 is 2120.
How to Find the LCM of 106 and 40 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 106 and 40 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, 106 and 40:
What are the Multiples of 106?
What are the Multiples of 40?
Let’s take a look at the first 10 multiples for each of these numbers, 106 and 40:
First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060
First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400
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 106 and 40 are 2120, 4240, 6360. Because 2120 is the smallest, it is the least common multiple.
The LCM of 106 and 40 is 2120.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 138 and 43?
What is the LCM of 19 and 147?
What is the LCM of 130 and 81?
What is the LCM of 31 and 109?
What is the LCM of 73 and 34?