Q:

What is the LCM of 35 and 17?

Accepted Solution

A:
Solution: The LCM of 35 and 17 is 595 Methods How to find the LCM of 35 and 17 using Prime Factorization One way to find the LCM of 35 and 17 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 35? What are the Factors of 17? Here is the prime factorization of 35: 5 1 × 7 1 5^1 × 7^1 5 1 × 7 1 And this is the prime factorization of 17: 1 7 1 17^1 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: 5, 7, 17 5 1 × 7 1 × 1 7 1 = 595 5^1 × 7^1 × 17^1 = 595 5 1 × 7 1 × 1 7 1 = 595 Through this we see that the LCM of 35 and 17 is 595. How to Find the LCM of 35 and 17 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 35 and 17 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, 35 and 17: What are the Multiples of 35? What are the Multiples of 17? Let’s take a look at the first 10 multiples for each of these numbers, 35 and 17: First 10 Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350 First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170 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 35 and 17 are 595, 1190, 1785. Because 595 is the smallest, it is the least common multiple. The LCM of 35 and 17 is 595. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 46 and 120? What is the LCM of 4 and 108? What is the LCM of 12 and 101? What is the LCM of 134 and 102? What is the LCM of 130 and 65?