Use scientific notation to determine which of these numbers has the least value: 123,893, 31,892, or 12,786. Write your answer in scientific notation, expressed to the exact decimal place.

To express the given numbers in scientific notation, we follow the format \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.

1. **For 123,893:**
\[
123,893 = 1.23893 \times 10^5
\]

2. **For 31,892:**
\[
31,892 = 3.1892 \times 10^4
\]

3. **For 12,786:**
\[
12,786 = 1.2786 \times 10^4
\]

Now we will compare all three values:

- \( 1.23893 \times 10^5 \) corresponds to 123,893.
- \( 3.1892 \times 10^4 \) corresponds to 31,892.
- \( 1.2786 \times 10^4 \) corresponds to 12,786.

Next, we compare the significant figures (the decimal parts) of the numbers in terms of magnitude:

- The first number \( 1.23893 \times 10^5 \) is in the range of \( 100,000 \) which is the highest value.
- The next two numbers are in the \( 10,000s \):
- \( 3.1892 \times 10^4 \) (approximately \( 31,892 \))
- \( 1.2786 \times 10^4 \) (approximately \( 12,786 \))

Since both of the last two numbers are multiplied by \( 10^4 \), we directly compare their coefficients:

- \( 3.1892 \) (for 31,892) is greater than \( 1.2786 \) (for 12,786).

Thus, the smallest number is \( 12,786 \).

Finally, expressing the least value in scientific notation:

\[
\boxed{1.2786 \times 10^4}
\]