Q:

What is the LCM of 126 and 93?

Accepted Solution

A:
Solution: The LCM of 126 and 93 is 3906MethodsHow to find the LCM of 126 and 93 using Prime FactorizationOne way to find the LCM of 126 and 93 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 126?What are the Factors of 93?Here is the prime factorization of 126:21×32×712^1 × 3^2 × 7^121×32×71And this is the prime factorization of 93:31×3113^1 × 31^131×311When 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, 7, 3121×32×71×311=39062^1 × 3^2 × 7^1 × 31^1 = 390621×32×71×311=3906Through this we see that the LCM of 126 and 93 is 3906.How to Find the LCM of 126 and 93 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 126 and 93 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, 126 and 93:What are the Multiples of 126?What are the Multiples of 93?Let’s take a look at the first 10 multiples for each of these numbers, 126 and 93:First 10 Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260First 10 Multiples of 93: 93, 186, 279, 372, 465, 558, 651, 744, 837, 930You 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 126 and 93 are 3906, 7812, 11718. Because 3906 is the smallest, it is the least common multiple.The LCM of 126 and 93 is 3906.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 51 and 92?What is the LCM of 61 and 24?What is the LCM of 71 and 119?What is the LCM of 28 and 33?What is the LCM of 81 and 7?