I was presented with the following problem:
What is the expected number of rolls of a $n$-sided die until i) the lcm of the rolls exceeds $k$? ii) the gcd of the rolls exceeds $k$?
Is this something that can be analytically done, or must this be done numerically?
As a hint, I am told that for $n=10$ and $k=2018$, the EV for part i) converges to $18.8$, but that seems oddly low.
Could someone prod me the right direction? Thanks!