Solution: The LCM of 87 and 143 is 12441
Methods
How to find the LCM of 87 and 143 using Prime Factorization
One way to find the LCM of 87 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 87?
What are the Factors of 143?
Here is the prime factorization of 87:
3
1
×
2
9
1
3^1 × 29^1
3 1 × 2 9 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: 3, 29, 11, 13
3
1
×
1
1
1
×
1
3
1
×
2
9
1
=
12441
3^1 × 11^1 × 13^1 × 29^1 = 12441
3 1 × 1 1 1 × 1 3 1 × 2 9 1 = 12441
Through this we see that the LCM of 87 and 143 is 12441.
How to Find the LCM of 87 and 143 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 87 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, 87 and 143:
What are the Multiples of 87?
What are the Multiples of 143?
Let’s take a look at the first 10 multiples for each of these numbers, 87 and 143:
First 10 Multiples of 87: 87, 174, 261, 348, 435, 522, 609, 696, 783, 870
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 87 and 143 are 12441, 24882, 37323. Because 12441 is the smallest, it is the least common multiple.
The LCM of 87 and 143 is 12441.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 93 and 41?
What is the LCM of 11 and 4?
What is the LCM of 2 and 7?
What is the LCM of 30 and 8?
What is the LCM of 59 and 145?