Solution: The LCM of 19 and 73 is 1387
Methods
How to find the LCM of 19 and 73 using Prime Factorization
One way to find the LCM of 19 and 73 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 73?
Here is the prime factorization of 19:
1
9
1
19^1
1 9 1
And this is the prime factorization of 73:
7
3
1
73^1
7 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: 19, 73
1
9
1
×
7
3
1
=
1387
19^1 × 73^1 = 1387
1 9 1 × 7 3 1 = 1387
Through this we see that the LCM of 19 and 73 is 1387.
How to Find the LCM of 19 and 73 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 19 and 73 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 73:
What are the Multiples of 19?
What are the Multiples of 73?
Let’s take a look at the first 10 multiples for each of these numbers, 19 and 73:
First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190
First 10 Multiples of 73: 73, 146, 219, 292, 365, 438, 511, 584, 657, 730
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 73 are 1387, 2774, 4161. Because 1387 is the smallest, it is the least common multiple.
The LCM of 19 and 73 is 1387.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 4 and 141?
What is the LCM of 2 and 101?
What is the LCM of 97 and 80?
What is the LCM of 33 and 50?
What is the LCM of 10 and 30?