The sum of the 12 scores is $12 \times 82 = 984$.
When the highest and lowest scores are removed, there are 10 scores remaining and the sum of these scores is $10 \times 84 = 840$.
Let the lowest score be $x$. The highest score is 98.
So, $984 - 98 - x = 840$.
Simplifying, we have $x = 46$.
Therefore, the lowest score is $\boxed{46}$.
The answer is: 46
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If the arithmetic mean of 12 scores is 82 and the mean increases to 84 when the highest and lowest scores are removed, with the highest score being 98, what is the lowest score?

### Answer:
