Q:

What is the LCM of 72 and 51?

Accepted Solution

A:
Solution: The LCM of 72 and 51 is 1224 Methods How to find the LCM of 72 and 51 using Prime Factorization One way to find the LCM of 72 and 51 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 72? What are the Factors of 51? Here is the prime factorization of 72: 2 3 × 3 2 2^3 × 3^2 2 3 × 3 2 And this is the prime factorization of 51: 3 1 × 1 7 1 3^1 × 17^1 3 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: 2, 3, 17 2 3 × 3 2 × 1 7 1 = 1224 2^3 × 3^2 × 17^1 = 1224 2 3 × 3 2 × 1 7 1 = 1224 Through this we see that the LCM of 72 and 51 is 1224. How to Find the LCM of 72 and 51 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 72 and 51 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, 72 and 51: What are the Multiples of 72? What are the Multiples of 51? Let’s take a look at the first 10 multiples for each of these numbers, 72 and 51: First 10 Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720 First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510 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 72 and 51 are 1224, 2448, 3672. Because 1224 is the smallest, it is the least common multiple. The LCM of 72 and 51 is 1224. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 9 and 53? What is the LCM of 74 and 102? What is the LCM of 70 and 55? What is the LCM of 119 and 42? What is the LCM of 21 and 22?