Q:

What is the LCM of 17 and 63?

Accepted Solution

A:
Solution: The LCM of 17 and 63 is 1071 Methods How to find the LCM of 17 and 63 using Prime Factorization One way to find the LCM of 17 and 63 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 17? What are the Factors of 63? Here is the prime factorization of 17: 1 7 1 17^1 1 7 1 And this is the prime factorization of 63: 3 2 × 7 1 3^2 × 7^1 3 2 × 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: 17, 3, 7 3 2 × 7 1 × 1 7 1 = 1071 3^2 × 7^1 × 17^1 = 1071 3 2 × 7 1 × 1 7 1 = 1071 Through this we see that the LCM of 17 and 63 is 1071. How to Find the LCM of 17 and 63 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 17 and 63 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, 17 and 63: What are the Multiples of 17? What are the Multiples of 63? Let’s take a look at the first 10 multiples for each of these numbers, 17 and 63: First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170 First 10 Multiples of 63: 63, 126, 189, 252, 315, 378, 441, 504, 567, 630 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 17 and 63 are 1071, 2142, 3213. Because 1071 is the smallest, it is the least common multiple. The LCM of 17 and 63 is 1071. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 20 and 6? What is the LCM of 54 and 13? What is the LCM of 45 and 83? What is the LCM of 81 and 37? What is the LCM of 123 and 118?