Q:

What is the LCM of 37 and 81?

Accepted Solution

A:
Solution: The LCM of 37 and 81 is 2997 Methods How to find the LCM of 37 and 81 using Prime Factorization One way to find the LCM of 37 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 37? What are the Factors of 81? Here is the prime factorization of 37: 3 7 1 37^1 3 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: 37, 3 3 4 × 3 7 1 = 2997 3^4 × 37^1 = 2997 3 4 × 3 7 1 = 2997 Through this we see that the LCM of 37 and 81 is 2997. How to Find the LCM of 37 and 81 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 37 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, 37 and 81: What are the Multiples of 37? What are the Multiples of 81? Let’s take a look at the first 10 multiples for each of these numbers, 37 and 81: First 10 Multiples of 37: 37, 74, 111, 148, 185, 222, 259, 296, 333, 370 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 37 and 81 are 2997, 5994, 8991. Because 2997 is the smallest, it is the least common multiple. The LCM of 37 and 81 is 2997. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 34 and 4? What is the LCM of 66 and 30? What is the LCM of 127 and 45? What is the LCM of 74 and 25? What is the LCM of 88 and 96?