Explanation

Lime (Calcium Hydroxide) is commonly used to precipitate and remove hardness-causing ions like calcium and magnesium. Sodium Carbonate can be used for softening but lime is a more direct agent mentioned in standard treatments. Alum is primarily used for coagulation, not directly for permanent hardness removal. Potassium Permanganate is an oxidizing agent and is not the primary chemical for removing permanent hardness.