Find the least 6-digit number exactly divisible by 83.

Answer

To find the least 6-digit number exactly divisible by 83, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the least 6-digit number**: The smallest 6-digit number is 100000.

2. **Divide this number by 83**: We need to find out how many times 83 fits into 100000.
\[ 100000 \div 83 \approx 1204.81928 \]
This means 83 fits into 100000 approximately 1204 times.

3. **Calculate the product of 83 and the integer part of the quotient**:
\[ 83 \times 1204 = 99932 \]
This is the largest 5-digit number that is divisible by 83.

4. **Find the remainder**:
\[ 100000 - 99932 = 68 \]
This means when we divide 100000 by 83, we have a remainder of 68.

5. **Calculate the least 6-digit number divisible by 83**:
To find the least 6-digit number that is divisible by 83, we need to add the difference to the next multiple of 83:
\[ 100000 + (83 - 68) = 100000 + 15 = 100015 \]

6. **Final answer**: Therefore, the least 6-digit number exactly divisible by 83 is **100015**.