Solution: The LCM of 34 and 62 is 1054
Methods
How to find the LCM of 34 and 62 using Prime Factorization
One way to find the LCM of 34 and 62 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 34?
What are the Factors of 62?
Here is the prime factorization of 34:
2
1
×
1
7
1
2^1 × 17^1
2 1 × 1 7 1
And this is the prime factorization of 62:
2
1
×
3
1
1
2^1 × 31^1
2 1 × 3 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, 17, 31
2
1
×
1
7
1
×
3
1
1
=
1054
2^1 × 17^1 × 31^1 = 1054
2 1 × 1 7 1 × 3 1 1 = 1054
Through this we see that the LCM of 34 and 62 is 1054.
How to Find the LCM of 34 and 62 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 34 and 62 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, 34 and 62:
What are the Multiples of 34?
What are the Multiples of 62?
Let’s take a look at the first 10 multiples for each of these numbers, 34 and 62:
First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340
First 10 Multiples of 62: 62, 124, 186, 248, 310, 372, 434, 496, 558, 620
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 34 and 62 are 1054, 2108, 3162. Because 1054 is the smallest, it is the least common multiple.
The LCM of 34 and 62 is 1054.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 147 and 123?
What is the LCM of 10 and 30?
What is the LCM of 69 and 149?
What is the LCM of 135 and 23?
What is the LCM of 80 and 4?