Q:

What is the LCM of 103 and 51?

Accepted Solution

A:
Solution: The LCM of 103 and 51 is 5253 Methods How to find the LCM of 103 and 51 using Prime Factorization One way to find the LCM of 103 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 103? What are the Factors of 51? Here is the prime factorization of 103: 10 3 1 103^1 10 3 1 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: 103, 3, 17 3 1 × 1 7 1 × 10 3 1 = 5253 3^1 × 17^1 × 103^1 = 5253 3 1 × 1 7 1 × 10 3 1 = 5253 Through this we see that the LCM of 103 and 51 is 5253. How to Find the LCM of 103 and 51 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 103 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, 103 and 51: What are the Multiples of 103? What are the Multiples of 51? Let’s take a look at the first 10 multiples for each of these numbers, 103 and 51: First 10 Multiples of 103: 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030 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 103 and 51 are 5253, 10506, 15759. Because 5253 is the smallest, it is the least common multiple. The LCM of 103 and 51 is 5253. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 149 and 43? What is the LCM of 68 and 20? What is the LCM of 17 and 22? What is the LCM of 54 and 8? What is the LCM of 36 and 87?