two friends met together at a club . After how many days will they meet again if one of them visits the club every 64 days and the other visits the club after every 72 days

To determine after how many days the two friends will meet again at the club, we need to find the **Least Common Multiple (LCM)** of the two time periods: 64 days and 72 days.

### Steps to find the LCM:

1. **Prime factorization**:
   - 64 = \( 2^6 \)
   - 72 = \( 2^3 \times 3^2 \)

2. **LCM formula**: 
   The LCM is found by taking the highest power of each prime factor that appears in the factorizations of the numbers.
   - For 2: Take \( 2^6 \) (since \( 2^6 \) is the highest power of 2 between the two numbers).
   - For 3: Take \( 3^2 \) (since \( 3^2 \) is the highest power of 3 between the two numbers).

3. **Multiply these together**:
   \[
   LCM = 2^6 \times 3^2 = 64 \times 9 = 576
   \]

Thus, the two friends will meet again after **576 days**.

---

Do you need any details or have any questions? Here are some related questions you might find interesting:

1. What is the greatest common divisor (GCD) of 64 and 72?
2. How do prime factorizations help in finding the LCM?
3. How would the result change if one of them visited the club every 100 days instead?
4. What if we had three friends visiting every 64, 72, and 80 days? How would we calculate the LCM then?
5. Can the LCM method be used for non-integer time intervals, like fractions?

**Tip**: The LCM is especially useful in problems involving repeating events over different intervals, like meeting schedules!

Two friends met together at a club. After how many days will they meet again if one of them visits the club every 64 days and the other visits the club every 72 days?

Find out how to calculate the Least Common Multiple (LCM) to determine after how many days two friends will meet again if one visits the club every 64 days and the other every 72 days. This example demonstrates prime factorization and the use of LCM for solving real-world problems. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation