Solution: The LCM of 141 and 72 is 3384
Methods
How to find the LCM of 141 and 72 using Prime Factorization
One way to find the LCM of 141 and 72 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 72?
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 72:
2
3
×
3
2
2^3 × 3^2
2 3 × 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
3
×
3
2
×
4
7
1
=
3384
2^3 × 3^2 × 47^1 = 3384
2 3 × 3 2 × 4 7 1 = 3384
Through this we see that the LCM of 141 and 72 is 3384.
How to Find the LCM of 141 and 72 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 141 and 72 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 72:
What are the Multiples of 141?
What are the Multiples of 72?
Let’s take a look at the first 10 multiples for each of these numbers, 141 and 72:
First 10 Multiples of 141: 141, 282, 423, 564, 705, 846, 987, 1128, 1269, 1410
First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720
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 72 are 3384, 6768, 10152. Because 3384 is the smallest, it is the least common multiple.
The LCM of 141 and 72 is 3384.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 140 and 25?
What is the LCM of 81 and 100?
What is the LCM of 21 and 73?
What is the LCM of 59 and 129?
What is the LCM of 55 and 75?