Problem #PRU-100238

Problem

Numbers $1,2,\dots ,20$ are written on a whiteboard. In one go Louise is allowed to wipe out any two numbers $a$ and $b$, and write instead

(a) $a+b-1$; (b) $a\times b$.

As you already know, Louise enjoys erasing the numbers, and has fun until only one number is left on the whiteboard. What number is it?