Q:

What is the LCM of 76 and 91?

Accepted Solution

A:
Solution: The LCM of 76 and 91 is 6916 Methods How to find the LCM of 76 and 91 using Prime Factorization One way to find the LCM of 76 and 91 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 76? What are the Factors of 91? Here is the prime factorization of 76: 2 2 × 1 9 1 2^2 × 19^1 2 2 × 1 9 1 And this is the prime factorization of 91: 7 1 × 1 3 1 7^1 × 13^1 7 1 × 1 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, 19, 7, 13 2 2 × 7 1 × 1 3 1 × 1 9 1 = 6916 2^2 × 7^1 × 13^1 × 19^1 = 6916 2 2 × 7 1 × 1 3 1 × 1 9 1 = 6916 Through this we see that the LCM of 76 and 91 is 6916. How to Find the LCM of 76 and 91 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 76 and 91 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, 76 and 91: What are the Multiples of 76? What are the Multiples of 91? Let’s take a look at the first 10 multiples for each of these numbers, 76 and 91: First 10 Multiples of 76: 76, 152, 228, 304, 380, 456, 532, 608, 684, 760 First 10 Multiples of 91: 91, 182, 273, 364, 455, 546, 637, 728, 819, 910 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 76 and 91 are 6916, 13832, 20748. Because 6916 is the smallest, it is the least common multiple. The LCM of 76 and 91 is 6916. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 10 and 103? What is the LCM of 112 and 96? What is the LCM of 80 and 49? What is the LCM of 132 and 122? What is the LCM of 71 and 63?