Q:

What is the LCM of 84 and 103?

Accepted Solution

A:
Solution: The LCM of 84 and 103 is 8652 Methods How to find the LCM of 84 and 103 using Prime Factorization One way to find the LCM of 84 and 103 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 84? What are the Factors of 103? Here is the prime factorization of 84: 2 2 × 3 1 × 7 1 2^2 × 3^1 × 7^1 2 2 × 3 1 × 7 1 And this is the prime factorization of 103: 10 3 1 103^1 10 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: 2, 3, 7, 103 2 2 × 3 1 × 7 1 × 10 3 1 = 8652 2^2 × 3^1 × 7^1 × 103^1 = 8652 2 2 × 3 1 × 7 1 × 10 3 1 = 8652 Through this we see that the LCM of 84 and 103 is 8652. How to Find the LCM of 84 and 103 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 84 and 103 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, 84 and 103: What are the Multiples of 84? What are the Multiples of 103? Let’s take a look at the first 10 multiples for each of these numbers, 84 and 103: First 10 Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840 First 10 Multiples of 103: 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030 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 84 and 103 are 8652, 17304, 25956. Because 8652 is the smallest, it is the least common multiple. The LCM of 84 and 103 is 8652. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 83 and 22? What is the LCM of 102 and 39? What is the LCM of 17 and 75? What is the LCM of 92 and 142? What is the LCM of 46 and 77?