Q:

What is the LCM of 77 and 86?

Accepted Solution

A:
Solution: The LCM of 77 and 86 is 6622 Methods How to find the LCM of 77 and 86 using Prime Factorization One way to find the LCM of 77 and 86 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 77? What are the Factors of 86? Here is the prime factorization of 77: 7 1 × 1 1 1 7^1 × 11^1 7 1 × 1 1 1 And this is the prime factorization of 86: 2 1 × 4 3 1 2^1 × 43^1 2 1 × 4 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: 7, 11, 2, 43 2 1 × 7 1 × 1 1 1 × 4 3 1 = 6622 2^1 × 7^1 × 11^1 × 43^1 = 6622 2 1 × 7 1 × 1 1 1 × 4 3 1 = 6622 Through this we see that the LCM of 77 and 86 is 6622. How to Find the LCM of 77 and 86 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 77 and 86 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, 77 and 86: What are the Multiples of 77? What are the Multiples of 86? Let’s take a look at the first 10 multiples for each of these numbers, 77 and 86: First 10 Multiples of 77: 77, 154, 231, 308, 385, 462, 539, 616, 693, 770 First 10 Multiples of 86: 86, 172, 258, 344, 430, 516, 602, 688, 774, 860 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 77 and 86 are 6622, 13244, 19866. Because 6622 is the smallest, it is the least common multiple. The LCM of 77 and 86 is 6622. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 63 and 9? What is the LCM of 18 and 87? What is the LCM of 150 and 50? What is the LCM of 97 and 49? What is the LCM of 31 and 32?