Q:

What is the LCM of 3 and 100?

Accepted Solution

A:
Solution: The LCM of 3 and 100 is 300 Methods How to find the LCM of 3 and 100 using Prime Factorization One way to find the LCM of 3 and 100 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 3? What are the Factors of 100? Here is the prime factorization of 3: 3 1 3^1 3 1 And this is the prime factorization of 100: 2 2 × 5 2 2^2 × 5^2 2 2 × 5 2 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: 3, 2, 5 2 2 × 3 1 × 5 2 = 300 2^2 × 3^1 × 5^2 = 300 2 2 × 3 1 × 5 2 = 300 Through this we see that the LCM of 3 and 100 is 300. How to Find the LCM of 3 and 100 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 3 and 100 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, 3 and 100: What are the Multiples of 3? What are the Multiples of 100? Let’s take a look at the first 10 multiples for each of these numbers, 3 and 100: First 10 Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 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 3 and 100 are 300, 600, 900. Because 300 is the smallest, it is the least common multiple. The LCM of 3 and 100 is 300. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 99 and 19? What is the LCM of 109 and 100? What is the LCM of 35 and 105? What is the LCM of 83 and 108? What is the LCM of 85 and 139?