A School Organizes Sporting Events For Different Classes Class A Has Events Every Nine Days Class B Every 12 Days And Class C Every 18 Days. If All Classes Have An Event On The Same Day Today, How Many Days Later All Classes

Feb 28, 2025 by ADMIN 225 views

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Introduction

In a school, different classes have their sporting events organized at different intervals. Class A has events every 9 days, Class B has events every 12 days, and Class C has events every 18 days. If all classes have an event on the same day today, we need to find out how many days later all classes will have an event on the same day again.

Understanding the Problem

To solve this problem, we need to find the least common multiple (LCM) of 9, 12, and 18. The LCM is the smallest number that is a multiple of all three numbers. This will give us the number of days after which all classes will have an event on the same day again.

Finding the Least Common Multiple (LCM)

To find the LCM of 9, 12, and 18, we need to first find the prime factors of each number.

9 = 3^2
12 = 2^2 * 3
18 = 2 * 3^2

Step 1: Identify the Common Prime Factors

The common prime factors of 9, 12, and 18 are 3 and 2.

Step 2: Determine the Highest Power of Each Prime Factor

The highest power of 3 is 3^2, and the highest power of 2 is 2^2.

Step 3: Multiply the Highest Powers of Each Prime Factor

To find the LCM, we multiply the highest powers of each prime factor.

LCM = 2^2 * 3^2 = 4 * 9 = 36

Conclusion

Therefore, all classes will have an event on the same day again in 36 days.

Real-World Applications

This problem has real-world applications in scheduling events, meetings, and appointments. It can be used to find the next time when multiple events will occur on the same day, which is useful in planning and organization.

Example Use Case

Suppose we have three teams, Team A, Team B, and Team C, that play a game every 9, 12, and 18 days, respectively. If all teams play a game on the same day today, we can use the LCM to find the next time when all teams will play a game on the same day again.

Code Implementation

Here is a Python code implementation to find the LCM:

import math

def find_lcm(num1, num2, num3):
    lcm = math.lcm(math.lcm(num1, num2), num3)
    return lcm

num1 = 9
num2 = 12
num3 = 18

lcm = find_lcm(num1, num2, num3)
print("The LCM of", num1, ",", num2, "and", num3, "is:", lcm)

Final Thoughts

In conclusion, finding the LCM of 9, 12, and 18 is a simple problem that can be solved using prime factorization and the concept of the least common multiple. This problem has real-world applications in scheduling events and can be used to find the next time when multiple events will occur on the same day.

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Introduction

In our previous article, we discussed how a school organizes sporting events for different classes, with Class A having events every 9 days, Class B having events every 12 days, and Class C having events every 18 days. We also found the least common multiple (LCM) of 9, 12, and 18, which is 36. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q1: What is the least common multiple (LCM) of 9, 12, and 18?

A1: The LCM of 9, 12, and 18 is 36.

Q2: How do you find the LCM of three numbers?

A2: To find the LCM of three numbers, you can first find the prime factors of each number, then identify the common prime factors, determine the highest power of each prime factor, and finally multiply the highest powers of each prime factor.

Q3: What is the significance of finding the LCM in real-world applications?

A3: Finding the LCM is significant in real-world applications such as scheduling events, meetings, and appointments. It can be used to find the next time when multiple events will occur on the same day, which is useful in planning and organization.

Q4: How can you use the LCM to find the next time when all classes will have an event on the same day again?

A4: You can use the LCM to find the next time when all classes will have an event on the same day again by adding the LCM to the current date.

Q5: What is the Python code implementation to find the LCM of three numbers?

A5: The Python code implementation to find the LCM of three numbers is as follows:

import math

def find_lcm(num1, num2, num3):
    lcm = math.lcm(math.lcm(num1, num2), num3)
    return lcm

num1 = 9
num2 = 12
num3 = 18

lcm = find_lcm(num1, num2, num3)
print("The LCM of", num1, ",", num2, "and", num3, "is:", lcm)

Q6: Can you explain the concept of prime factorization in finding the LCM?

A6: Yes, prime factorization is the process of breaking down a number into its prime factors. For example, the prime factorization of 9 is 3^2, the prime factorization of 12 is 2^2 * 3, and the prime factorization of 18 is 2 * 3^2.

Q7: How do you determine the highest power of each prime factor in finding the LCM?

A7: To determine the highest power of each prime factor, you need to identify the highest power of each prime factor that appears in the prime factorization of the three numbers.

Q8: Can you provide an example use case of finding the LCM in real-world applications?

A8: Yes, an example use case of finding the LCM is in scheduling events, meetings, and appointments. Suppose we have three teams, Team A, Team B, and Team C, that play a game every 9, 12, and 18 days, respectively. If all teams play a game on the same day today, we can use the LCM to find the next time when all teams will play a game on the same day again.