Q:

What is the LCM of 8 and 15?

Accepted Solution

A:
Solution: The LCM of 8 and 15 is 120 Methods How to find the LCM of 8 and 15 using Prime Factorization One way to find the LCM of 8 and 15 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 8? What are the Factors of 15? Here is the prime factorization of 8: 2 3 2^3 2 3 And this is the prime factorization of 15: 3 1 × 5 1 3^1 × 5^1 3 1 × 5 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: 2, 3, 5 2 3 × 3 1 × 5 1 = 120 2^3 × 3^1 × 5^1 = 120 2 3 × 3 1 × 5 1 = 120 Through this we see that the LCM of 8 and 15 is 120. How to Find the LCM of 8 and 15 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 8 and 15 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, 8 and 15: What are the Multiples of 8? What are the Multiples of 15? Let’s take a look at the first 10 multiples for each of these numbers, 8 and 15: First 10 Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 First 10 Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 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 8 and 15 are 120, 240, 360. Because 120 is the smallest, it is the least common multiple. The LCM of 8 and 15 is 120. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 108 and 93? What is the LCM of 76 and 115? What is the LCM of 38 and 37? What is the LCM of 104 and 122? What is the LCM of 110 and 1?