Solution: The LCM of 47 and 134 is 6298
Methods
How to find the LCM of 47 and 134 using Prime Factorization
One way to find the LCM of 47 and 134 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 47?
What are the Factors of 134?
Here is the prime factorization of 47:
4
7
1
47^1
4 7 1
And this is the prime factorization of 134:
2
1
×
6
7
1
2^1 × 67^1
2 1 × 6 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: 47, 2, 67
2
1
×
4
7
1
×
6
7
1
=
6298
2^1 × 47^1 × 67^1 = 6298
2 1 × 4 7 1 × 6 7 1 = 6298
Through this we see that the LCM of 47 and 134 is 6298.
How to Find the LCM of 47 and 134 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 47 and 134 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, 47 and 134:
What are the Multiples of 47?
What are the Multiples of 134?
Let’s take a look at the first 10 multiples for each of these numbers, 47 and 134:
First 10 Multiples of 47: 47, 94, 141, 188, 235, 282, 329, 376, 423, 470
First 10 Multiples of 134: 134, 268, 402, 536, 670, 804, 938, 1072, 1206, 1340
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 47 and 134 are 6298, 12596, 18894. Because 6298 is the smallest, it is the least common multiple.
The LCM of 47 and 134 is 6298.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 129 and 52?
What is the LCM of 121 and 76?
What is the LCM of 5 and 91?
What is the LCM of 31 and 67?
What is the LCM of 78 and 41?