Solution: The LCM of 40 and 143 is 5720
Methods
How to find the LCM of 40 and 143 using Prime Factorization
One way to find the LCM of 40 and 143 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 143?
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 143:
1
1
1
×
1
3
1
11^1 × 13^1
1 1 1 × 1 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: 2, 5, 11, 13
2
3
×
5
1
×
1
1
1
×
1
3
1
=
5720
2^3 × 5^1 × 11^1 × 13^1 = 5720
2 3 × 5 1 × 1 1 1 × 1 3 1 = 5720
Through this we see that the LCM of 40 and 143 is 5720.
How to Find the LCM of 40 and 143 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 40 and 143 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 143:
What are the Multiples of 40?
What are the Multiples of 143?
Let’s take a look at the first 10 multiples for each of these numbers, 40 and 143:
First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400
First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430
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 143 are 5720, 11440, 17160. Because 5720 is the smallest, it is the least common multiple.
The LCM of 40 and 143 is 5720.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 79 and 47?
What is the LCM of 113 and 33?
What is the LCM of 72 and 71?
What is the LCM of 107 and 134?
What is the LCM of 91 and 115?