+510 An eccentric baseball card collector wants to distribute her collection among her descendants. If she divided her cards among her $13$ great-great-grandchildren, there would be $8$ cards left over. If she divided her cards among her $10$ great-grandchildren, there would be $2$ cards left over. If she divided her cards among her fve grandchildren, there would be $4$ cards left over. If she divided her cards among her three children, there would be $2$ cards left over.
What is the smallest possible number of cards in her collection?
