Burlesque, 18 bytes

f:qsv^mjlnm{)gv<]}

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f:   # Count frequency (as {count val}) in gridqsv  # Save in global map^m   # Apply to each frequencyj    # Swapln   # Split into linesm{   # Map over words )gv # Map over each letter get value from global map<]  # Minimum}