You only need one hamper for the entire lot. TS4's laundry system works by 'Lot' not by room. The hamper can even be in the basement and all clothes will auto be placed in there.
If you do not place a washer, dryer or hand tub on your lot then washing will never be generated but you could place them on a community lot, do your washing there and then your sim will have to bring it home and 'put away' once on the home lot, thereby giving your sims the moodlets.
The quicker you put your washing away once done the higher the modlets/cleanliness will be. e.g. pristine washing left in a dryer will deteriorate to clean then eventually all the way to foul if left long enough.
Conversely, if you like realism you can place a dryer/washer on your lot and no hamper so that all your sims clothes will end up on the floor creating very life-like teen rooms.
Leave washing there for a day or two and <bingo> the perfect smelly teens room.