Solution: The LCM of 19 and 84 is 1596
Methods
How to find the LCM of 19 and 84 using Prime Factorization
One way to find the LCM of 19 and 84 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 84?
Here is the prime factorization of 19:
1
9
1
19^1
1 9 1
And this is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 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: 19, 2, 3, 7
2
2
×
3
1
×
7
1
×
1
9
1
=
1596
2^2 × 3^1 × 7^1 × 19^1 = 1596
2 2 × 3 1 × 7 1 × 1 9 1 = 1596
Through this we see that the LCM of 19 and 84 is 1596.
How to Find the LCM of 19 and 84 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 19 and 84 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 84:
What are the Multiples of 19?
What are the Multiples of 84?
Let’s take a look at the first 10 multiples for each of these numbers, 19 and 84:
First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190
First 10 Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840
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 84 are 1596, 3192, 4788. Because 1596 is the smallest, it is the least common multiple.
The LCM of 19 and 84 is 1596.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 30 and 8?
What is the LCM of 113 and 13?
What is the LCM of 65 and 121?
What is the LCM of 67 and 33?
What is the LCM of 38 and 23?