Q:

What is the LCM of 105 and 81?

Accepted Solution

A:
Solution: The LCM of 105 and 81 is 2835 Methods How to find the LCM of 105 and 81 using Prime Factorization One way to find the LCM of 105 and 81 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 81? Here is the prime factorization of 105: 3 1 × 5 1 × 7 1 3^1 × 5^1 × 7^1 3 1 × 5 1 × 7 1 And this is the prime factorization of 81: 3 4 3^4 3 4 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 3 4 × 5 1 × 7 1 = 2835 3^4 × 5^1 × 7^1 = 2835 3 4 × 5 1 × 7 1 = 2835 Through this we see that the LCM of 105 and 81 is 2835. How to Find the LCM of 105 and 81 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 105 and 81 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 81: What are the Multiples of 105? What are the Multiples of 81? Let’s take a look at the first 10 multiples for each of these numbers, 105 and 81: First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050 First 10 Multiples of 81: 81, 162, 243, 324, 405, 486, 567, 648, 729, 810 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 81 are 2835, 5670, 8505. Because 2835 is the smallest, it is the least common multiple. The LCM of 105 and 81 is 2835. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 14 and 78? What is the LCM of 41 and 139? What is the LCM of 76 and 71? What is the LCM of 118 and 31? What is the LCM of 13 and 75?