Q:

What is the LCM of 78 and 125?

Accepted Solution

A:
Solution: The LCM of 78 and 125 is 9750 Methods How to find the LCM of 78 and 125 using Prime Factorization One way to find the LCM of 78 and 125 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 125? 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 125: 5 3 5^3 5 3 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, 5 2 1 × 3 1 × 5 3 × 1 3 1 = 9750 2^1 × 3^1 × 5^3 × 13^1 = 9750 2 1 × 3 1 × 5 3 × 1 3 1 = 9750 Through this we see that the LCM of 78 and 125 is 9750. How to Find the LCM of 78 and 125 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 78 and 125 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 125: What are the Multiples of 78? What are the Multiples of 125? Let’s take a look at the first 10 multiples for each of these numbers, 78 and 125: First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780 First 10 Multiples of 125: 125, 250, 375, 500, 625, 750, 875, 1000, 1125, 1250 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 125 are 9750, 19500, 29250. Because 9750 is the smallest, it is the least common multiple. The LCM of 78 and 125 is 9750. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 27 and 141? What is the LCM of 68 and 34? What is the LCM of 1 and 82? What is the LCM of 15 and 40? What is the LCM of 10 and 4?