Learn Italian: Gli armadietti si devono chiudere con un lucchetto.

In this sentence, we are using the si passivante (passive "si"). Because the action is being done to gli armadietti (the lockers), they act as the grammatical subject of the sentence. Since gli armadietti is plural, the modal verb dovere must be conjugated in the plural form (devono).

Could the "si" be placed somewhere else in this sentence?

Yes! When you have a modal verb (like dovere, potere, or volere) followed by an infinitive verb, you can also attach the si to the end of the infinitive. To do this, you drop the final "e" of the infinitive. So, you could also say Gli armadietti devono chiudersi con un lucchetto, and it means exactly the same thing.

What if the sentence was only about a single locker? How would the grammar change?

If the noun were singular (l'armadietto), the modal verb would have to change to the singular form to match it. The sentence would become: L'armadietto si deve chiudere con un lucchetto. In a si passivante construction, you must always match the verb to the noun receiving the action!

I recognize the word armadio (wardrobe) inside armadietti. Are they related?