Solution: The LCM of 19 and 99 is 1881
Methods
How to find the LCM of 19 and 99 using Prime Factorization
One way to find the LCM of 19 and 99 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 19?
What are the Factors of 99?
Here is the prime factorization of 19:
1
9
1
19^1
1 9 1
And this is the prime factorization of 99:
3
2
×
1
1
1
3^2 × 11^1
3 2 × 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: 19, 3, 11
3
2
×
1
1
1
×
1
9
1
=
1881
3^2 × 11^1 × 19^1 = 1881
3 2 × 1 1 1 × 1 9 1 = 1881
Through this we see that the LCM of 19 and 99 is 1881.
How to Find the LCM of 19 and 99 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 19 and 99 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, 19 and 99:
What are the Multiples of 19?
What are the Multiples of 99?
Let’s take a look at the first 10 multiples for each of these numbers, 19 and 99:
First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190
First 10 Multiples of 99: 99, 198, 297, 396, 495, 594, 693, 792, 891, 990
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 19 and 99 are 1881, 3762, 5643. Because 1881 is the smallest, it is the least common multiple.
The LCM of 19 and 99 is 1881.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 133 and 149?
What is the LCM of 57 and 78?
What is the LCM of 137 and 100?
What is the LCM of 116 and 115?
What is the LCM of 147 and 32?