Q:

What is the LCM of 132 and 73?

Accepted Solution

A:
Solution: The LCM of 132 and 73 is 9636MethodsHow to find the LCM of 132 and 73 using Prime FactorizationOne way to find the LCM of 132 and 73 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 132?What are the Factors of 73?Here is the prime factorization of 132:22×31×1112^2 × 3^1 × 11^122×31×111And this is the prime factorization of 73:73173^1731When 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, 3, 11, 7322×31×111×731=96362^2 × 3^1 × 11^1 × 73^1 = 963622×31×111×731=9636Through this we see that the LCM of 132 and 73 is 9636.How to Find the LCM of 132 and 73 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 132 and 73 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, 132 and 73:What are the Multiples of 132?What are the Multiples of 73?Let’s take a look at the first 10 multiples for each of these numbers, 132 and 73:First 10 Multiples of 132: 132, 264, 396, 528, 660, 792, 924, 1056, 1188, 1320First 10 Multiples of 73: 73, 146, 219, 292, 365, 438, 511, 584, 657, 730You 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 132 and 73 are 9636, 19272, 28908. Because 9636 is the smallest, it is the least common multiple.The LCM of 132 and 73 is 9636.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 137 and 14?What is the LCM of 34 and 58?What is the LCM of 146 and 3?What is the LCM of 37 and 103?What is the LCM of 142 and 43?