Question 6
For every positive integer $x$, denote by $\kappa(x)$ the number of composite numbers not greater than $x$. Find all positive integers $n$ such that
$$
(\kappa(n))! \cdot \text{lcm}(1,2,\dots,n) \gt (n-1)!
$$
$$
(\kappa(n))! \cdot \text{lcm}(1,2,\dots,n) \gt (n-1)!
$$