Repeating greetings to a gathering
Anas (radi Allahu anhu) reported, the Prophet (sal Allahu alaihi wa sallam) used to repeat his words thrice so that the meaning thereof would be fully understood, and whenever he came upon a gathering of people, he would greet them. He would repeat Salam three times.
This Hadith tells us about one aspect of the Prophet’s (sal Allahu alaihi wa sallam) excellent manners that he would take due care of showing regard for the sentiments of people.
The whole of a gathering is not supposed to hear the Salam of somebody and respond to him. A single person can represent the gathering in this regard, yet, it was characteristic benevolence of the Messenger of Allah (sal Allahu alaihi wa sallam) which prompted him to repeat his saying “As-Salamu ‘Alaikum” thrice so that everybody would hear it and may not have a feeling of being neglected.
And Allah knows best!