Solution: The LCM of 93 and 110 is 10230
Methods
How to find the LCM of 93 and 110 using Prime Factorization
One way to find the LCM of 93 and 110 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 93?
What are the Factors of 110?
Here is the prime factorization of 93:
3
1
×
3
1
1
3^1 × 31^1
3 1 × 3 1 1
And this is the prime factorization of 110:
2
1
×
5
1
×
1
1
1
2^1 × 5^1 × 11^1
2 1 × 5 1 × 1 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: 3, 31, 2, 5, 11
2
1
×
3
1
×
5
1
×
1
1
1
×
3
1
1
=
10230
2^1 × 3^1 × 5^1 × 11^1 × 31^1 = 10230
2 1 × 3 1 × 5 1 × 1 1 1 × 3 1 1 = 10230
Through this we see that the LCM of 93 and 110 is 10230.
How to Find the LCM of 93 and 110 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 93 and 110 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, 93 and 110:
What are the Multiples of 93?
What are the Multiples of 110?
Let’s take a look at the first 10 multiples for each of these numbers, 93 and 110:
First 10 Multiples of 93: 93, 186, 279, 372, 465, 558, 651, 744, 837, 930
First 10 Multiples of 110: 110, 220, 330, 440, 550, 660, 770, 880, 990, 1100
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 93 and 110 are 10230, 20460, 30690. Because 10230 is the smallest, it is the least common multiple.
The LCM of 93 and 110 is 10230.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 139 and 72?
What is the LCM of 36 and 92?
What is the LCM of 1 and 47?
What is the LCM of 67 and 137?
What is the LCM of 103 and 136?