Q:

What is the LCM of 17 and 68?

Accepted Solution

A:
Solution: The LCM of 17 and 68 is 68 Methods How to find the LCM of 17 and 68 using Prime Factorization One way to find the LCM of 17 and 68 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 68? Here is the prime factorization of 17: 1 7 1 17^1 1 7 1 And this is the prime factorization of 68: 2 2 × 1 7 1 2^2 × 17^1 2 2 × 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: 17, 2 2 2 × 1 7 1 = 68 2^2 × 17^1 = 68 2 2 × 1 7 1 = 68 Through this we see that the LCM of 17 and 68 is 68. How to Find the LCM of 17 and 68 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 17 and 68 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 68: What are the Multiples of 17? What are the Multiples of 68? Let’s take a look at the first 10 multiples for each of these numbers, 17 and 68: First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170 First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680 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 68 are 68, 136, 204. Because 68 is the smallest, it is the least common multiple. The LCM of 17 and 68 is 68. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 5 and 147? What is the LCM of 140 and 138? What is the LCM of 146 and 109? What is the LCM of 93 and 58? What is the LCM of 46 and 36?