Q:

What is the LCM of 51 and 18?

Accepted Solution

A:
Solution: The LCM of 51 and 18 is 306 Methods How to find the LCM of 51 and 18 using Prime Factorization One way to find the LCM of 51 and 18 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 51? What are the Factors of 18? Here is the prime factorization of 51: 3 1 × 1 7 1 3^1 × 17^1 3 1 × 1 7 1 And this is the prime factorization of 18: 2 1 × 3 2 2^1 × 3^2 2 1 × 3 2 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, 17, 2 2 1 × 3 2 × 1 7 1 = 306 2^1 × 3^2 × 17^1 = 306 2 1 × 3 2 × 1 7 1 = 306 Through this we see that the LCM of 51 and 18 is 306. How to Find the LCM of 51 and 18 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 51 and 18 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, 51 and 18: What are the Multiples of 51? What are the Multiples of 18? Let’s take a look at the first 10 multiples for each of these numbers, 51 and 18: First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510 First 10 Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180 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 51 and 18 are 306, 612, 918. Because 306 is the smallest, it is the least common multiple. The LCM of 51 and 18 is 306. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 68 and 56? What is the LCM of 124 and 10? What is the LCM of 64 and 133? What is the LCM of 107 and 19? What is the LCM of 22 and 35?