Q:

What is the LCM of 65 and 25?

Accepted Solution

A:
Solution: The LCM of 65 and 25 is 325MethodsHow to find the LCM of 65 and 25 using Prime FactorizationOne way to find the LCM of 65 and 25 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 25?Here is the prime factorization of 65:51×1315^1 × 13^151×131And this is the prime factorization of 25:525^252When 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, 1352×131=3255^2 × 13^1 = 32552×131=325Through this we see that the LCM of 65 and 25 is 325.How to Find the LCM of 65 and 25 by Listing Common MultiplesThe first step to this method of finding the Least Common Multiple of 65 and 25 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 25:What are the Multiples of 65?What are the Multiples of 25?Let’s take a look at the first 10 multiples for each of these numbers, 65 and 25:First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650First 10 Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250You 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 25 are 325, 650, 975. Because 325 is the smallest, it is the least common multiple.The LCM of 65 and 25 is 325.Find the LCM of Other Number PairsWant more practice? Try some of these other LCM problems:What is the LCM of 39 and 14?What is the LCM of 95 and 97?What is the LCM of 15 and 3?What is the LCM of 13 and 66?What is the LCM of 11 and 20?