Q:

What is the LCM of 28 and 102?

Accepted Solution

A:
Solution: The LCM of 28 and 102 is 1428 Methods How to find the LCM of 28 and 102 using Prime Factorization One way to find the LCM of 28 and 102 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 28? What are the Factors of 102? Here is the prime factorization of 28: 2 2 × 7 1 2^2 × 7^1 2 2 × 7 1 And this 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 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, 7, 3, 17 2 2 × 3 1 × 7 1 × 1 7 1 = 1428 2^2 × 3^1 × 7^1 × 17^1 = 1428 2 2 × 3 1 × 7 1 × 1 7 1 = 1428 Through this we see that the LCM of 28 and 102 is 1428. How to Find the LCM of 28 and 102 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 28 and 102 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, 28 and 102: What are the Multiples of 28? What are the Multiples of 102? Let’s take a look at the first 10 multiples for each of these numbers, 28 and 102: First 10 Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280 First 10 Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020 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 28 and 102 are 1428, 2856, 4284. Because 1428 is the smallest, it is the least common multiple. The LCM of 28 and 102 is 1428. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 130 and 46? What is the LCM of 144 and 35? What is the LCM of 48 and 100? What is the LCM of 82 and 30? What is the LCM of 33 and 41?