Solution: The LCM of 101 and 34 is 3434
Methods
How to find the LCM of 101 and 34 using Prime Factorization
One way to find the LCM of 101 and 34 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 101?
What are the Factors of 34?
Here is the prime factorization of 101:
10
1
1
101^1
10 1 1
And this is the prime factorization of 34:
2
1
×
1
7
1
2^1 × 17^1
2 1 × 1 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: 101, 2, 17
2
1
×
1
7
1
×
10
1
1
=
3434
2^1 × 17^1 × 101^1 = 3434
2 1 × 1 7 1 × 10 1 1 = 3434
Through this we see that the LCM of 101 and 34 is 3434.
How to Find the LCM of 101 and 34 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 101 and 34 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, 101 and 34:
What are the Multiples of 101?
What are the Multiples of 34?
Let’s take a look at the first 10 multiples for each of these numbers, 101 and 34:
First 10 Multiples of 101: 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010
First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340
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 101 and 34 are 3434, 6868, 10302. Because 3434 is the smallest, it is the least common multiple.
The LCM of 101 and 34 is 3434.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 12 and 150?
What is the LCM of 94 and 111?
What is the LCM of 112 and 64?
What is the LCM of 109 and 114?
What is the LCM of 10 and 79?