Solution: The LCM of 40 and 124 is 1240
Methods
How to find the LCM of 40 and 124 using Prime Factorization
One way to find the LCM of 40 and 124 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 124?
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 124:
2
2
×
3
1
1
2^2 × 31^1
2 2 × 3 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: 2, 5, 31
2
3
×
5
1
×
3
1
1
=
1240
2^3 × 5^1 × 31^1 = 1240
2 3 × 5 1 × 3 1 1 = 1240
Through this we see that the LCM of 40 and 124 is 1240.
How to Find the LCM of 40 and 124 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 40 and 124 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 124:
What are the Multiples of 40?
What are the Multiples of 124?
Let’s take a look at the first 10 multiples for each of these numbers, 40 and 124:
First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400
First 10 Multiples of 124: 124, 248, 372, 496, 620, 744, 868, 992, 1116, 1240
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 124 are 1240, 2480, 3720. Because 1240 is the smallest, it is the least common multiple.
The LCM of 40 and 124 is 1240.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 17 and 134?
What is the LCM of 37 and 63?
What is the LCM of 15 and 137?
What is the LCM of 19 and 80?
What is the LCM of 76 and 104?