Q:

What is the LCM of 102 and 30?

Accepted Solution

A:
Solution: The LCM of 102 and 30 is 510 Methods How to find the LCM of 102 and 30 using Prime Factorization One way to find the LCM of 102 and 30 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 102? What are the Factors of 30? Here is the prime factorization of 102: 2 1 × 3 1 × 1 7 1 2^1 × 3^1 × 17^1 2 1 × 3 1 × 1 7 1 And this is the prime factorization of 30: 2 1 × 3 1 × 5 1 2^1 × 3^1 × 5^1 2 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, 17, 5 2 1 × 3 1 × 5 1 × 1 7 1 = 510 2^1 × 3^1 × 5^1 × 17^1 = 510 2 1 × 3 1 × 5 1 × 1 7 1 = 510 Through this we see that the LCM of 102 and 30 is 510. How to Find the LCM of 102 and 30 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 102 and 30 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, 102 and 30: What are the Multiples of 102? What are the Multiples of 30? Let’s take a look at the first 10 multiples for each of these numbers, 102 and 30: First 10 Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020 First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300 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 102 and 30 are 510, 1020, 1530. Because 510 is the smallest, it is the least common multiple. The LCM of 102 and 30 is 510. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 24 and 119? What is the LCM of 49 and 150? What is the LCM of 44 and 56? What is the LCM of 40 and 57? What is the LCM of 97 and 94?