Mishkat al-Masabih
Anas said that when the Prophet (ﷺ) made a statement he repeated it three times so that it would be understood, and that when he met a company and gave them a salutation he did it three times. Bukhari transmitted it.
وَعَنْ أَنَسٍ قَالَ: كَانَ النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ إِذَا تَكَلَّمَ بِكَلِمَةٍ أَعَادَهَا ثَلَاثًا حَتَّى تُفْهَمَ عَنْهُ وَإِذَا أَتَى عَلَى قَوْمٍ فَسَلَّمَ عَلَيْهِمْ سَلَّمَ عَلَيْهِمْ ثَلَاثًا ". رَوَاهُ الْبُخَارِيُّ
Reference