Solution: The LCM of 38 and 71 is 2698
Methods
How to find the LCM of 38 and 71 using Prime Factorization
One way to find the LCM of 38 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 38?
What are the Factors of 71?
Here is the prime factorization of 38:
2
1
×
1
9
1
2^1 × 19^1
2 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: 2, 19, 71
2
1
×
1
9
1
×
7
1
1
=
2698
2^1 × 19^1 × 71^1 = 2698
2 1 × 1 9 1 × 7 1 1 = 2698
Through this we see that the LCM of 38 and 71 is 2698.
How to Find the LCM of 38 and 71 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 38 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, 38 and 71:
What are the Multiples of 38?
What are the Multiples of 71?
Let’s take a look at the first 10 multiples for each of these numbers, 38 and 71:
First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380
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 38 and 71 are 2698, 5396, 8094. Because 2698 is the smallest, it is the least common multiple.
The LCM of 38 and 71 is 2698.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 132 and 56?
What is the LCM of 27 and 143?
What is the LCM of 99 and 125?
What is the LCM of 89 and 123?
What is the LCM of 94 and 113?