Sahih Muslim Book 23, Hadith Number 5039.

Chapter : The merit of licking the fingers after taking food and wiping the dish (with fingers) and eating of the fallen mouthful after removing the dirt sticking to it.

Ibn Ka’b b. Malik reported on the authority of his father that he saw Allah’s Messenger (may peace be upon him) licking his three fingers (after having finished the food). Ibn Hatim made no mention of “three”. This hadith is also narrated through another chain of transmitters.