https://file.aiquickdraw.com/mathbot/file/1727385587765zlbbotrt.jpg

The problem asks to find the least number of cups and plates that need to be purchased so that there are the same number of each. Cups are sold in packages of 6, and plates are sold in packages of 8. To solve this, you need to find the **Least Common Multiple (LCM)** of 6 and 8.

The solution written shows:

1. **Prime factorization:**
   - 6 = 2 × 3
   - 8 = 2³

2. **LCM calculation:**
   The LCM is found by taking the highest power of all prime factors involved:
   - The highest power of 2 is \( 2^3 \) (from 8).
   - The highest power of 3 is \( 3^1 \) (from 6).

   Therefore, the LCM = \( 2^3 \times 3 = 8 \times 3 = 24 \).

But the final solution shown on the worksheet suggests \( 32 \), which looks like an error. The correct LCM is **24**, meaning you need 24 cups and 24 plates to have the same number.

Would you like more details or have any questions?

### 5 Questions:
1. How do you calculate the greatest common factor (GCF) compared to the LCM?
2. Why is LCM used in this type of problem and not GCF?
3. Can you explain how prime factorization helps in finding the LCM?
4. What would happen if the number of items per package changed?
5. How do you verify that 24 is the smallest number for both cups and plates?

### Tip:
When solving LCM problems, always double-check that you're using the largest powers of all prime factors involved.

Cups are sold 6 to a package and plates are sold 8 to a package. If you want to have the same number of each item for a party, what is the least number of cups/plates you need to have?

Learn how to calculate the least common multiple (LCM) for packages of cups sold in 6 and plates sold in 8. Find the least number of cups and plates needed for a party. This problem uses prime factorization and LCM concepts suitable for Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation