Solution: The LCM of 141 and 144 is 6768
Methods
How to find the LCM of 141 and 144 using Prime Factorization
One way to find the LCM of 141 and 144 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 141?
What are the Factors of 144?
Here is the prime factorization of 141:
3
1
×
4
7
1
3^1 × 47^1
3 1 × 4 7 1
And this is the prime factorization of 144:
2
4
×
3
2
2^4 × 3^2
2 4 × 3 2
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, 47, 2
2
4
×
3
2
×
4
7
1
=
6768
2^4 × 3^2 × 47^1 = 6768
2 4 × 3 2 × 4 7 1 = 6768
Through this we see that the LCM of 141 and 144 is 6768.
How to Find the LCM of 141 and 144 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 141 and 144 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, 141 and 144:
What are the Multiples of 141?
What are the Multiples of 144?
Let’s take a look at the first 10 multiples for each of these numbers, 141 and 144:
First 10 Multiples of 141: 141, 282, 423, 564, 705, 846, 987, 1128, 1269, 1410
First 10 Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440
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 141 and 144 are 6768, 13536, 20304. Because 6768 is the smallest, it is the least common multiple.
The LCM of 141 and 144 is 6768.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 12 and 76?
What is the LCM of 7 and 63?
What is the LCM of 133 and 10?
What is the LCM of 96 and 128?
What is the LCM of 68 and 71?