Solution: The LCM of 19 and 68 is 1292
Methods
How to find the LCM of 19 and 68 using Prime Factorization
One way to find the LCM of 19 and 68 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 68?
Here is the prime factorization of 19:
1
9
1
19^1
1 9 1
And this is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 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, 17
2
2
×
1
7
1
×
1
9
1
=
1292
2^2 × 17^1 × 19^1 = 1292
2 2 × 1 7 1 × 1 9 1 = 1292
Through this we see that the LCM of 19 and 68 is 1292.
How to Find the LCM of 19 and 68 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 19 and 68 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 68:
What are the Multiples of 19?
What are the Multiples of 68?
Let’s take a look at the first 10 multiples for each of these numbers, 19 and 68:
First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190
First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680
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 68 are 1292, 2584, 3876. Because 1292 is the smallest, it is the least common multiple.
The LCM of 19 and 68 is 1292.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 62 and 122?
What is the LCM of 37 and 102?
What is the LCM of 28 and 61?
What is the LCM of 108 and 35?
What is the LCM of 111 and 49?