Find the smallest 5-digit number which is exactly divisible by 384.

To find the smallest 5-digit number that is exactly divisible by 384, follow these steps:

1. Identify the range of 5-digit numbers:

   • The smallest 5-digit number is 10000.
   • The largest 5-digit number is 99999.

2. Determine the smallest 5-digit number divisible by 384:

   • To find the smallest 5-digit number divisible by 384, we need to divide 10000 by 384 and round up to the nearest whole number. This will give us the smallest integer that, when multiplied by 384, results in a number greater than or equal to 10000.

3. Perform the division: $\frac{10000}{384} \approx 26.0417$

   • Since we need to round up to the nearest whole number, we get 27.

4. Multiply the rounded-up quotient by 384: $27 \times 384 = 10368$

5. Verify the result:

   • 10368 is a 5-digit number.
   • To confirm it is divisible by 384, we can perform the division: $\frac{10368}{384} = 27$
   • Since the result is an integer, 10368 is indeed divisible by 384.

Therefore, the smallest 5-digit number that is exactly divisible by 384 is 10368.