Q:

What is the LCM of 127 and 132?

Accepted Solution

A:
Solution: The LCM of 127 and 132 is 16764MethodsHow to find the LCM of 127 and 132 using Prime FactorizationOne way to find the LCM of 127 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 127?What are the Factors of 132?Here is the prime factorization of 127:1271127^11271And this is the prime factorization of 132:22×31×1112^2 × 3^1 × 11^122×31×111When 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: 127, 2, 3, 1122×31×111×1271=167642^2 × 3^1 × 11^1 × 127^1 = 1676422×31×111×1271=16764Through this we see that the LCM of 127 and 132 is 16764.How to Find the LCM of 127 and 132 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 127 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, 127 and 132:What are the Multiples of 127?What are the Multiples of 132?Let’s take a look at the first 10 multiples for each of these numbers, 127 and 132:First 10 Multiples of 127: 127, 254, 381, 508, 635, 762, 889, 1016, 1143, 1270First 10 Multiples of 132: 132, 264, 396, 528, 660, 792, 924, 1056, 1188, 1320You 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 127 and 132 are 16764, 33528, 50292. Because 16764 is the smallest, it is the least common multiple.The LCM of 127 and 132 is 16764.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 109 and 71?What is the LCM of 119 and 16?What is the LCM of 53 and 88?What is the LCM of 93 and 23?What is the LCM of 17 and 7?