Q:

What is the LCM of 97 and 84?

Accepted Solution

A:
Solution: The LCM of 97 and 84 is 8148 Methods How to find the LCM of 97 and 84 using Prime Factorization One way to find the LCM of 97 and 84 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 97? What are the Factors of 84? Here is the prime factorization of 97: 9 7 1 97^1 9 7 1 And this is the prime factorization of 84: 2 2 × 3 1 × 7 1 2^2 × 3^1 × 7^1 2 2 × 3 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: 97, 2, 3, 7 2 2 × 3 1 × 7 1 × 9 7 1 = 8148 2^2 × 3^1 × 7^1 × 97^1 = 8148 2 2 × 3 1 × 7 1 × 9 7 1 = 8148 Through this we see that the LCM of 97 and 84 is 8148. How to Find the LCM of 97 and 84 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 97 and 84 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, 97 and 84: What are the Multiples of 97? What are the Multiples of 84? Let’s take a look at the first 10 multiples for each of these numbers, 97 and 84: First 10 Multiples of 97: 97, 194, 291, 388, 485, 582, 679, 776, 873, 970 First 10 Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840 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 97 and 84 are 8148, 16296, 24444. Because 8148 is the smallest, it is the least common multiple. The LCM of 97 and 84 is 8148. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 63 and 6? What is the LCM of 42 and 140? What is the LCM of 113 and 73? What is the LCM of 76 and 41? What is the LCM of 110 and 24?