I never saw the Prophet ﷺ laughing to an extent that one could see his palate, but he always used to smile only.  

مَا رَأَيْتُ النَّبِيَّ ﷺ مُسْتَجْمِعًا قَطُّ ضَاحِكًا حَتَّى أَرَى مِنْهُ لَهَوَاتِهِ إِنَّمَا كَانَ يَتَبَسَّمُ