Solution: The LCM of 58 and 77 is 4466
Methods
How to find the LCM of 58 and 77 using Prime Factorization
One way to find the LCM of 58 and 77 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 58?
What are the Factors of 77?
Here is the prime factorization of 58:
2
1
×
2
9
1
2^1 × 29^1
2 1 × 2 9 1
And this is the prime factorization of 77:
7
1
×
1
1
1
7^1 × 11^1
7 1 × 1 1 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: 2, 29, 7, 11
2
1
×
7
1
×
1
1
1
×
2
9
1
=
4466
2^1 × 7^1 × 11^1 × 29^1 = 4466
2 1 × 7 1 × 1 1 1 × 2 9 1 = 4466
Through this we see that the LCM of 58 and 77 is 4466.
How to Find the LCM of 58 and 77 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 58 and 77 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, 58 and 77:
What are the Multiples of 58?
What are the Multiples of 77?
Let’s take a look at the first 10 multiples for each of these numbers, 58 and 77:
First 10 Multiples of 58: 58, 116, 174, 232, 290, 348, 406, 464, 522, 580
First 10 Multiples of 77: 77, 154, 231, 308, 385, 462, 539, 616, 693, 770
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 58 and 77 are 4466, 8932, 13398. Because 4466 is the smallest, it is the least common multiple.
The LCM of 58 and 77 is 4466.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 112 and 62?
What is the LCM of 109 and 73?
What is the LCM of 128 and 96?
What is the LCM of 41 and 92?
What is the LCM of 48 and 46?