Problem #WSP-000349

Problem

A gang of three jewel thieves has stolen some gold coins and wants to divide them fairly. However, they each have one unusual rule: (i) The first thief wants the number of coins to be divisible by $3$ so they can split it evenly. (ii) The second thief wants the number of coins to be divisible by $5$ because she wants to split her share with her four siblings. (iii) The third thief wants the number of coins to be divisible by $7$ since he wants to split his share amongst seven company stocks.

However, they’re stuck as the number of coins isn’t divisible by any of these numbers. In fact, the number of coins is $1$ more than a multiple of $3$, $3$ more than a multiple of $5$ and $5$ more than a multiple of $7$.
What’s the smallest number of coins they could have? (And if you’re feeling generous, how would you help them out?)