Solution: The LCM of 102 and 71 is 7242
Methods
How to find the LCM of 102 and 71 using Prime Factorization
One way to find the LCM of 102 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 102?
What are the Factors of 71?
Here is the prime factorization of 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 1 × 1 7 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, 3, 17, 71
2
1
×
3
1
×
1
7
1
×
7
1
1
=
7242
2^1 × 3^1 × 17^1 × 71^1 = 7242
2 1 × 3 1 × 1 7 1 × 7 1 1 = 7242
Through this we see that the LCM of 102 and 71 is 7242.
How to Find the LCM of 102 and 71 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 102 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, 102 and 71:
What are the Multiples of 102?
What are the Multiples of 71?
Let’s take a look at the first 10 multiples for each of these numbers, 102 and 71:
First 10 Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020
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 102 and 71 are 7242, 14484, 21726. Because 7242 is the smallest, it is the least common multiple.
The LCM of 102 and 71 is 7242.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 13 and 64?
What is the LCM of 46 and 112?
What is the LCM of 15 and 141?
What is the LCM of 67 and 144?
What is the LCM of 21 and 52?