Q:

What is the LCM of 97 and 40?

Accepted Solution

A:
Solution: The LCM of 97 and 40 is 3880MethodsHow to find the LCM of 97 and 40 using Prime FactorizationOne way to find the LCM of 97 and 40 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 97?What are the Factors of 40?Here is the prime factorization of 97:97197^1971And this is the prime factorization of 40:23×512^3 × 5^123×51When 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: 97, 2, 523×51×971=38802^3 × 5^1 × 97^1 = 388023×51×971=3880Through this we see that the LCM of 97 and 40 is 3880.How to Find the LCM of 97 and 40 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 97 and 40 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, 97 and 40:What are the Multiples of 97?What are the Multiples of 40?Let’s take a look at the first 10 multiples for each of these numbers, 97 and 40:First 10 Multiples of 97: 97, 194, 291, 388, 485, 582, 679, 776, 873, 970First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400You 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 97 and 40 are 3880, 7760, 11640. Because 3880 is the smallest, it is the least common multiple.The LCM of 97 and 40 is 3880.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 24 and 112?What is the LCM of 130 and 104?What is the LCM of 40 and 32?What is the LCM of 39 and 50?What is the LCM of 28 and 2?