The smallest 5-digit number that is divisible by 19 is

Options

A. 10019
B. 10013
C. 10032
D. 10000

Answer

To find the smallest 5-digit number that is divisible by 19, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the smallest 5-digit number**:
The smallest 5-digit number is 10,000.

2. **Divide 10,000 by 19**:
We need to determine how many times 19 fits into 10,000.
\[ 10,000 \div 19 \approx 526.315789 \]
The integer part of this division is 526.

3. **Multiply 526 by 19**:
Now, we multiply 526 by 19 to find the largest multiple of 19 that is less than or equal to 10,000.
\[ 526 \times 19 = 9,994 \]

4. **Calculate the remainder**:
Next, we find the remainder when 10,000 is divided by 19.
\[ 10,000 - 9,994 = 6 \]

5. **Find the next multiple of 19**:
Since there is a remainder of 6, we need to add enough to 10,000 to reach the next multiple of 19. We need to add \(19 - 6 = 13\).
\[ 10,000 + 13 = 10,013 \]

6. **Conclusion**:
Therefore, the smallest 5-digit number that is divisible by 19 is **10,013**.

### Final Answer:
The smallest 5-digit number that is divisible by 19 is **10,013**.