Solution: The LCM of 50 and 134 is 3350
Methods
How to find the LCM of 50 and 134 using Prime Factorization
One way to find the LCM of 50 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 50?
What are the Factors of 134?
Here is the prime factorization of 50:
2
1
×
5
2
2^1 × 5^2
2 1 × 5 2
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: 2, 5, 67
2
1
×
5
2
×
6
7
1
=
3350
2^1 × 5^2 × 67^1 = 3350
2 1 × 5 2 × 6 7 1 = 3350
Through this we see that the LCM of 50 and 134 is 3350.
How to Find the LCM of 50 and 134 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 50 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, 50 and 134:
What are the Multiples of 50?
What are the Multiples of 134?
Let’s take a look at the first 10 multiples for each of these numbers, 50 and 134:
First 10 Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500
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 50 and 134 are 3350, 6700, 10050. Because 3350 is the smallest, it is the least common multiple.
The LCM of 50 and 134 is 3350.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 110 and 105?
What is the LCM of 141 and 41?
What is the LCM of 62 and 67?
What is the LCM of 125 and 31?
What is the LCM of 119 and 9?