Q:

What is the LCM of 78 and 63?

Accepted Solution

A:
Solution: The LCM of 78 and 63 is 1638 Methods How to find the LCM of 78 and 63 using Prime Factorization One way to find the LCM of 78 and 63 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 78? What are the Factors of 63? Here is the prime factorization of 78: 2 1 × 3 1 × 1 3 1 2^1 × 3^1 × 13^1 2 1 × 3 1 × 1 3 1 And this is the prime factorization of 63: 3 2 × 7 1 3^2 × 7^1 3 2 × 7 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, 13, 7 2 1 × 3 2 × 7 1 × 1 3 1 = 1638 2^1 × 3^2 × 7^1 × 13^1 = 1638 2 1 × 3 2 × 7 1 × 1 3 1 = 1638 Through this we see that the LCM of 78 and 63 is 1638. How to Find the LCM of 78 and 63 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 78 and 63 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, 78 and 63: What are the Multiples of 78? What are the Multiples of 63? Let’s take a look at the first 10 multiples for each of these numbers, 78 and 63: First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780 First 10 Multiples of 63: 63, 126, 189, 252, 315, 378, 441, 504, 567, 630 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 78 and 63 are 1638, 3276, 4914. Because 1638 is the smallest, it is the least common multiple. The LCM of 78 and 63 is 1638. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 25 and 96? What is the LCM of 118 and 141? What is the LCM of 112 and 80? What is the LCM of 15 and 144? What is the LCM of 66 and 6?