Solution: The LCM of 11 and 47 is 517
Methods
How to find the LCM of 11 and 47 using Prime Factorization
One way to find the LCM of 11 and 47 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 11?
What are the Factors of 47?
Here is the prime factorization of 11:
1
1
1
11^1
1 1 1
And this is the prime factorization of 47:
4
7
1
47^1
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: 11, 47
1
1
1
×
4
7
1
=
517
11^1 × 47^1 = 517
1 1 1 × 4 7 1 = 517
Through this we see that the LCM of 11 and 47 is 517.
How to Find the LCM of 11 and 47 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 11 and 47 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, 11 and 47:
What are the Multiples of 11?
What are the Multiples of 47?
Let’s take a look at the first 10 multiples for each of these numbers, 11 and 47:
First 10 Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110
First 10 Multiples of 47: 47, 94, 141, 188, 235, 282, 329, 376, 423, 470
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 11 and 47 are 517, 1034, 1551. Because 517 is the smallest, it is the least common multiple.
The LCM of 11 and 47 is 517.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 1 and 30?
What is the LCM of 109 and 93?
What is the LCM of 104 and 112?
What is the LCM of 148 and 127?
What is the LCM of 116 and 131?