Q:

What is the LCM of 27 and 38?

Accepted Solution

A:
Solution: The LCM of 27 and 38 is 1026 Methods How to find the LCM of 27 and 38 using Prime Factorization One way to find the LCM of 27 and 38 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 27? What are the Factors of 38? Here is the prime factorization of 27: 3 3 3^3 3 3 And this is the prime factorization of 38: 2 1 × 1 9 1 2^1 × 19^1 2 1 × 1 9 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: 3, 2, 19 2 1 × 3 3 × 1 9 1 = 1026 2^1 × 3^3 × 19^1 = 1026 2 1 × 3 3 × 1 9 1 = 1026 Through this we see that the LCM of 27 and 38 is 1026. How to Find the LCM of 27 and 38 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 27 and 38 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, 27 and 38: What are the Multiples of 27? What are the Multiples of 38? Let’s take a look at the first 10 multiples for each of these numbers, 27 and 38: First 10 Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270 First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380 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 27 and 38 are 1026, 2052, 3078. Because 1026 is the smallest, it is the least common multiple. The LCM of 27 and 38 is 1026. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 134 and 147? What is the LCM of 101 and 2? What is the LCM of 130 and 137? What is the LCM of 14 and 63? What is the LCM of 70 and 94?