Solution: The LCM of 77 and 141 is 10857
Methods
How to find the LCM of 77 and 141 using Prime Factorization
One way to find the LCM of 77 and 141 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 77?
What are the Factors of 141?
Here is the prime factorization of 77:
7
1
×
1
1
1
7^1 × 11^1
7 1 × 1 1 1
And this is the prime factorization of 141:
3
1
×
4
7
1
3^1 × 47^1
3 1 × 4 7 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: 7, 11, 3, 47
3
1
×
7
1
×
1
1
1
×
4
7
1
=
10857
3^1 × 7^1 × 11^1 × 47^1 = 10857
3 1 × 7 1 × 1 1 1 × 4 7 1 = 10857
Through this we see that the LCM of 77 and 141 is 10857.
How to Find the LCM of 77 and 141 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 77 and 141 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, 77 and 141:
What are the Multiples of 77?
What are the Multiples of 141?
Let’s take a look at the first 10 multiples for each of these numbers, 77 and 141:
First 10 Multiples of 77: 77, 154, 231, 308, 385, 462, 539, 616, 693, 770
First 10 Multiples of 141: 141, 282, 423, 564, 705, 846, 987, 1128, 1269, 1410
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 77 and 141 are 10857, 21714, 32571. Because 10857 is the smallest, it is the least common multiple.
The LCM of 77 and 141 is 10857.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 37 and 32?
What is the LCM of 52 and 115?
What is the LCM of 149 and 21?
What is the LCM of 25 and 146?
What is the LCM of 126 and 84?