Suppose a lecture hall has a rectangular array of chairs with \(r\) rows and \(c\) columns. Suppose further that there are precisely \(19\) girls seated in each row and precisely \(15\) boys seated in each column.
If exactly \(14\) chairs are empty then find the minimum possible value of \(r \times c.\)
Details and Assumptions:
- A maximum of one person per chair is allowed.