Which one of the following equals the product of the smallest prime number greater than 21 and the largest prime number less than 16?

Options

A. `13 cdot 16`
B. `13 cdot 29`
C. `13 cdot 23`
D. `15 cdot 23`

Answer

To solve the problem, we need to find two prime numbers: the smallest prime number greater than 21 and the largest prime number less than 16. Then, we will calculate the product of these two prime numbers.

### Step-by-Step Solution:

1. **Identify the smallest prime number greater than 21**:
- The prime numbers greater than 21 are: 23, 29, 31, ...
- The smallest prime number in this list is **23**.

2. **Identify the largest prime number less than 16**:
- The prime numbers less than 16 are: 2, 3, 5, 7, 11, 13.
- The largest prime number in this list is **13**.

3. **Calculate the product of these two prime numbers**:
- Now, we need to find the product of 23 and 13.
- \( 23 \times 13 = 299 \).

4. **Check the options provided**:
- Option A: \( 13 \times 16 \) = 208
- Option B: \( 13 \times 29 \) = 377
- Option C: \( 13 \times 23 \) = 299
- Option D: \( 15 \times 23 \) = 345

5. **Identify the correct option**:
- From our calculation, \( 13 \times 23 = 299 \), which matches with **Option C**.

### Final Answer:
The correct answer is **Option C: 13 x 23**.