HeY ppl! I have a senario I need to solve but need some help from you guyz! I'm at like step 2!

The senario is: A band of 17 pirates stole a sack of coins. When they tried to divide them equally among them, 3 coins remained. In the brawl that followed, one pirate was killed. Again, they tried to divide the coins equally among themselves only to find 10 coins remaining. Another pirate was killed! Now, upon dividing the coins, none was left. What is the minimum number of coins that the pirates could have been distributing.

So far all i know is that you use the Chinese Remainder theorem and you get a set of equations... ->

x = 3mod17

x = 10mod16

x = 0mod15

Anyone know how to solve this?!