Q:

What is the LCM of 106 and 91?

Accepted Solution

A:
Solution: The LCM of 106 and 91 is 9646 Methods How to find the LCM of 106 and 91 using Prime Factorization One way to find the LCM of 106 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 106? What are the Factors of 91? Here is the prime factorization of 106: 2 1 × 5 3 1 2^1 × 53^1 2 1 × 5 3 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, 53, 7, 13 2 1 × 7 1 × 1 3 1 × 5 3 1 = 9646 2^1 × 7^1 × 13^1 × 53^1 = 9646 2 1 × 7 1 × 1 3 1 × 5 3 1 = 9646 Through this we see that the LCM of 106 and 91 is 9646. How to Find the LCM of 106 and 91 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 106 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, 106 and 91: What are the Multiples of 106? What are the Multiples of 91? Let’s take a look at the first 10 multiples for each of these numbers, 106 and 91: First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060 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 106 and 91 are 9646, 19292, 28938. Because 9646 is the smallest, it is the least common multiple. The LCM of 106 and 91 is 9646. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 141 and 84? What is the LCM of 113 and 150? What is the LCM of 101 and 67? What is the LCM of 65 and 137? What is the LCM of 33 and 11?