Q:

What is the LCM of 105 and 85?

Accepted Solution

A:
Solution: The LCM of 105 and 85 is 1785 Methods How to find the LCM of 105 and 85 using Prime Factorization One way to find the LCM of 105 and 85 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 105? What are the Factors of 85? Here is the prime factorization of 105: 3 1 Γ— 5 1 Γ— 7 1 3^1 Γ— 5^1 Γ— 7^1 3 1 Γ— 5 1 Γ— 7 1 And this is the prime factorization of 85: 5 1 Γ— 1 7 1 5^1 Γ— 17^1 5 1 Γ— 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: 3, 5, 7, 17 3 1 Γ— 5 1 Γ— 7 1 Γ— 1 7 1 = 1785 3^1 Γ— 5^1 Γ— 7^1 Γ— 17^1 = 1785 3 1 Γ— 5 1 Γ— 7 1 Γ— 1 7 1 = 1785 Through this we see that the LCM of 105 and 85 is 1785. How to Find the LCM of 105 and 85 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 105 and 85 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, 105 and 85: What are the Multiples of 105? What are the Multiples of 85? Let’s take a look at the first 10 multiples for each of these numbers, 105 and 85: First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050 First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850 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 105 and 85 are 1785, 3570, 5355. Because 1785 is the smallest, it is the least common multiple. The LCM of 105 and 85 is 1785. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 28 and 69? What is the LCM of 59 and 135? What is the LCM of 85 and 75? What is the LCM of 117 and 48? What is the LCM of 97 and 103?