Q:

What is the LCM of 65 and 51?

Accepted Solution

A:
Solution: The LCM of 65 and 51 is 3315 Methods How to find the LCM of 65 and 51 using Prime Factorization One way to find the LCM of 65 and 51 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 51? Here is the prime factorization of 65: 5 1 × 1 3 1 5^1 × 13^1 5 1 × 1 3 1 And this is the prime factorization of 51: 3 1 × 1 7 1 3^1 × 17^1 3 1 × 1 7 1 When 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, 3, 17 3 1 × 5 1 × 1 3 1 × 1 7 1 = 3315 3^1 × 5^1 × 13^1 × 17^1 = 3315 3 1 × 5 1 × 1 3 1 × 1 7 1 = 3315 Through this we see that the LCM of 65 and 51 is 3315. How to Find the LCM of 65 and 51 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 65 and 51 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 51: What are the Multiples of 65? What are the Multiples of 51? Let’s take a look at the first 10 multiples for each of these numbers, 65 and 51: First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650 First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510 You 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 51 are 3315, 6630, 9945. Because 3315 is the smallest, it is the least common multiple. The LCM of 65 and 51 is 3315. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 39 and 58? What is the LCM of 31 and 29? What is the LCM of 107 and 140? What is the LCM of 85 and 10? What is the LCM of 100 and 86?