Solution: The LCM of 19 and 71 is 1349
Methods
How to find the LCM of 19 and 71 using Prime Factorization
One way to find the LCM of 19 and 71 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 71?
Here is the prime factorization of 19:
1
9
1
19^1
1 9 1
And this is the prime factorization of 71:
7
1
1
71^1
7 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, 71
1
9
1
×
7
1
1
=
1349
19^1 × 71^1 = 1349
1 9 1 × 7 1 1 = 1349
Through this we see that the LCM of 19 and 71 is 1349.
How to Find the LCM of 19 and 71 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 19 and 71 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 71:
What are the Multiples of 19?
What are the Multiples of 71?
Let’s take a look at the first 10 multiples for each of these numbers, 19 and 71:
First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190
First 10 Multiples of 71: 71, 142, 213, 284, 355, 426, 497, 568, 639, 710
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 71 are 1349, 2698, 4047. Because 1349 is the smallest, it is the least common multiple.
The LCM of 19 and 71 is 1349.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 45 and 65?
What is the LCM of 133 and 12?
What is the LCM of 58 and 20?
What is the LCM of 52 and 11?
What is the LCM of 83 and 114?