Let's

Let $n$ be a positive integer such that there exists positive integers $x$ and $y$ satisfying $\begin{cases} \text{lcm}(x,y) =n! \\ \gcd(x,y) = 1998 \end{cases}$

Which of the following options is true?

$$ Notations:

• $\text{lcm}(\cdot)$ denotes the lowest common multiple function.

• $\gcd(\cdot)$ denotes the greatest common divisor function.

• $!$ is the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .