Q:

What is the LCM of 102 and 45?

Accepted Solution

A:
Solution: The LCM of 102 and 45 is 1530 Methods How to find the LCM of 102 and 45 using Prime Factorization One way to find the LCM of 102 and 45 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 45? 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 45: 3 2 × 5 1 3^2 × 5^1 3 2 × 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 2 × 5 1 × 1 7 1 = 1530 2^1 × 3^2 × 5^1 × 17^1 = 1530 2 1 × 3 2 × 5 1 × 1 7 1 = 1530 Through this we see that the LCM of 102 and 45 is 1530. How to Find the LCM of 102 and 45 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 102 and 45 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 45: What are the Multiples of 102? What are the Multiples of 45? Let’s take a look at the first 10 multiples for each of these numbers, 102 and 45: First 10 Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020 First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450 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 45 are 1530, 3060, 4590. Because 1530 is the smallest, it is the least common multiple. The LCM of 102 and 45 is 1530. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 114 and 129? What is the LCM of 76 and 93? What is the LCM of 36 and 141? What is the LCM of 143 and 14? What is the LCM of 12 and 20?