Q:

What is the LCM of 91 and 132?

Accepted Solution

A:
Solution: The LCM of 91 and 132 is 12012 Methods How to find the LCM of 91 and 132 using Prime Factorization One way to find the LCM of 91 and 132 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 91? What are the Factors of 132? Here is the prime factorization of 91: 7 1 × 1 3 1 7^1 × 13^1 7 1 × 1 3 1 And this is the prime factorization of 132: 2 2 × 3 1 × 1 1 1 2^2 × 3^1 × 11^1 2 2 × 3 1 × 1 1 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, 13, 2, 3, 11 2 2 × 3 1 × 7 1 × 1 1 1 × 1 3 1 = 12012 2^2 × 3^1 × 7^1 × 11^1 × 13^1 = 12012 2 2 × 3 1 × 7 1 × 1 1 1 × 1 3 1 = 12012 Through this we see that the LCM of 91 and 132 is 12012. How to Find the LCM of 91 and 132 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 91 and 132 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, 91 and 132: What are the Multiples of 91? What are the Multiples of 132? Let’s take a look at the first 10 multiples for each of these numbers, 91 and 132: First 10 Multiples of 91: 91, 182, 273, 364, 455, 546, 637, 728, 819, 910 First 10 Multiples of 132: 132, 264, 396, 528, 660, 792, 924, 1056, 1188, 1320 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 91 and 132 are 12012, 24024, 36036. Because 12012 is the smallest, it is the least common multiple. The LCM of 91 and 132 is 12012. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 72 and 16? What is the LCM of 78 and 70? What is the LCM of 137 and 133? What is the LCM of 101 and 32? What is the LCM of 29 and 145?