Solution: The LCM of 6 and 101 is 606
Methods
How to find the LCM of 6 and 101 using Prime Factorization
One way to find the LCM of 6 and 101 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 6?
What are the Factors of 101?
Here is the prime factorization of 6:
2
1
×
3
1
2^1 × 3^1
2 1 × 3 1
And this is the prime factorization of 101:
10
1
1
101^1
10 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, 3, 101
2
1
×
3
1
×
10
1
1
=
606
2^1 × 3^1 × 101^1 = 606
2 1 × 3 1 × 10 1 1 = 606
Through this we see that the LCM of 6 and 101 is 606.
How to Find the LCM of 6 and 101 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 6 and 101 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, 6 and 101:
What are the Multiples of 6?
What are the Multiples of 101?
Let’s take a look at the first 10 multiples for each of these numbers, 6 and 101:
First 10 Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
First 10 Multiples of 101: 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010
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 6 and 101 are 606, 1212, 1818. Because 606 is the smallest, it is the least common multiple.
The LCM of 6 and 101 is 606.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 60 and 43?
What is the LCM of 61 and 114?
What is the LCM of 134 and 27?
What is the LCM of 106 and 105?
What is the LCM of 82 and 73?