Many little divisors

Determine the largest integer $$n$$ that is divisible by all positive integers (strictly) less than $$\dfrac{\sqrt{n}}{2}$$.

As an example, for $$n = 36$$, $$\frac{\sqrt{n}}{2} = 3$$, and all positive integers less than it ($$1$$ and $$2$$) divide $$n$$, so it is one candidate. Find the largest one.

If there is no such largest integer (there's an arbitrarily large one), answer 0 instead.

×