Solution: The LCM of 105 and 91 is 1365
Methods
How to find the LCM of 105 and 91 using Prime Factorization
One way to find the LCM of 105 and 91 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 105?
What are the Factors of 91?
Here is the prime factorization of 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 1 × 7 1
And this is the prime factorization of 91:
7
1
×
1
3
1
7^1 × 13^1
7 1 × 1 3 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: 3, 5, 7, 13
3
1
×
5
1
×
7
1
×
1
3
1
=
1365
3^1 × 5^1 × 7^1 × 13^1 = 1365
3 1 × 5 1 × 7 1 × 1 3 1 = 1365
Through this we see that the LCM of 105 and 91 is 1365.
How to Find the LCM of 105 and 91 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 105 and 91 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, 105 and 91:
What are the Multiples of 105?
What are the Multiples of 91?
Let’s take a look at the first 10 multiples for each of these numbers, 105 and 91:
First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050
First 10 Multiples of 91: 91, 182, 273, 364, 455, 546, 637, 728, 819, 910
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 105 and 91 are 1365, 2730, 4095. Because 1365 is the smallest, it is the least common multiple.
The LCM of 105 and 91 is 1365.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 77 and 16?
What is the LCM of 70 and 20?
What is the LCM of 141 and 92?
What is the LCM of 120 and 114?
What is the LCM of 117 and 125?