Q:

What is the LCM of 10 and 64?

Accepted Solution

A:
Solution: The LCM of 10 and 64 is 320 Methods How to find the LCM of 10 and 64 using Prime Factorization One way to find the LCM of 10 and 64 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 10? What are the Factors of 64? Here is the prime factorization of 10: 2 1 × 5 1 2^1 × 5^1 2 1 × 5 1 And this is the prime factorization of 64: 2 6 2^6 2 6 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: 2, 5 2 6 × 5 1 = 320 2^6 × 5^1 = 320 2 6 × 5 1 = 320 Through this we see that the LCM of 10 and 64 is 320. How to Find the LCM of 10 and 64 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 10 and 64 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, 10 and 64: What are the Multiples of 10? What are the Multiples of 64? Let’s take a look at the first 10 multiples for each of these numbers, 10 and 64: First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 First 10 Multiples of 64: 64, 128, 192, 256, 320, 384, 448, 512, 576, 640 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 10 and 64 are 320, 640, 960. Because 320 is the smallest, it is the least common multiple. The LCM of 10 and 64 is 320. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 49 and 41? What is the LCM of 24 and 34? What is the LCM of 69 and 83? What is the LCM of 38 and 14? What is the LCM of 62 and 3?