Q:

What is the LCM of 9 and 53?

Accepted Solution

A:
Solution: The LCM of 9 and 53 is 477 Methods How to find the LCM of 9 and 53 using Prime Factorization One way to find the LCM of 9 and 53 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 9? What are the Factors of 53? Here is the prime factorization of 9: 3 2 3^2 3 2 And this is the prime factorization of 53: 5 3 1 53^1 5 3 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, 53 3 2 × 5 3 1 = 477 3^2 × 53^1 = 477 3 2 × 5 3 1 = 477 Through this we see that the LCM of 9 and 53 is 477. How to Find the LCM of 9 and 53 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 9 and 53 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, 9 and 53: What are the Multiples of 9? What are the Multiples of 53? Let’s take a look at the first 10 multiples for each of these numbers, 9 and 53: First 10 Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 First 10 Multiples of 53: 53, 106, 159, 212, 265, 318, 371, 424, 477, 530 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 9 and 53 are 477, 954, 1431. Because 477 is the smallest, it is the least common multiple. The LCM of 9 and 53 is 477. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 68 and 114? What is the LCM of 82 and 125? What is the LCM of 70 and 67? What is the LCM of 144 and 93? What is the LCM of 109 and 102?