Q:

What is the LCM of 65 and 62?

Accepted Solution

A:
Solution: The LCM of 65 and 62 is 4030MethodsHow to find the LCM of 65 and 62 using Prime FactorizationOne way to find the LCM of 65 and 62 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 65?What are the Factors of 62?Here is the prime factorization of 65:51×1315^1 × 13^151×131And this is the prime factorization of 62:21×3112^1 × 31^121×311When 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: 5, 13, 2, 3121×51×131×311=40302^1 × 5^1 × 13^1 × 31^1 = 403021×51×131×311=4030Through this we see that the LCM of 65 and 62 is 4030.How to Find the LCM of 65 and 62 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 65 and 62 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, 65 and 62:What are the Multiples of 65?What are the Multiples of 62?Let’s take a look at the first 10 multiples for each of these numbers, 65 and 62:First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650First 10 Multiples of 62: 62, 124, 186, 248, 310, 372, 434, 496, 558, 620You 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 65 and 62 are 4030, 8060, 12090. Because 4030 is the smallest, it is the least common multiple.The LCM of 65 and 62 is 4030.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 104 and 28?What is the LCM of 64 and 48?What is the LCM of 127 and 123?What is the LCM of 29 and 15?What is the LCM of 40 and 10?