The minimum gun for naval shore bombardment

What is the minimum useful gun caliber for coastal bombardment in a modern conflict?

A 4.5-inch or 5-inch gun is preferred for supporting troops ashore, although smaller guns can serve limited bombardment missions.

The required calibre depends on the fire mission. Guns of 76 mm or about 105 mm can be sufficient in some situations. For sustained support of forces going ashore, the preference is for a 4.5-inch or 5-inch gun. The 127 mm weapon mentioned in the question is the 5-inch option.