Solution: The LCM of 143 and 48 is 6864
Methods
How to find the LCM of 143 and 48 using Prime Factorization
One way to find the LCM of 143 and 48 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 143?
What are the Factors of 48?
Here is the prime factorization of 143:
1
1
1
Γ
1
3
1
11^1 Γ 13^1
1 1 1 Γ 1 3 1
And this is the prime factorization of 48:
2
4
Γ
3
1
2^4 Γ 3^1
2 4 Γ 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: 11, 13, 2, 3
2
4
Γ
3
1
Γ
1
1
1
Γ
1
3
1
=
6864
2^4 Γ 3^1 Γ 11^1 Γ 13^1 = 6864
2 4 Γ 3 1 Γ 1 1 1 Γ 1 3 1 = 6864
Through this we see that the LCM of 143 and 48 is 6864.
How to Find the LCM of 143 and 48 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 143 and 48 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.
Letβs take a look at the multiples for each of these numbers, 143 and 48:
What are the Multiples of 143?
What are the Multiples of 48?
Letβs take a look at the first 10 multiples for each of these numbers, 143 and 48:
First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430
First 10 Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, 480
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 143 and 48 are 6864, 13728, 20592. Because 6864 is the smallest, it is the least common multiple.
The LCM of 143 and 48 is 6864.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 8 and 94?
What is the LCM of 40 and 144?
What is the LCM of 33 and 78?
What is the LCM of 93 and 51?
What is the LCM of 132 and 84?