Ella has a collection of coins.  When she puts the coins in piles of $4$, there are $3$ left over.  When she puts the coins in piles of $5$, there are $3$ left over.  When she puts the coins in piles of $7$, there are $3$ left over.  When she puts the coins in piles of $9$, there is no remainder.  How many coins does she have at least? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem->Step-by-step Calculation