Problem: If the number 15!, that is, 15⋅14⋅13⋯1, ends with k zeros when given to the base 12 and ends with h zeros when given to the base 10, then k+h equals:
Answer Choices:
A. 5
B. 6
C. 7
D. 8
E. 9
Solution:
15!=103(3⋅14⋅13⋅12⋅11⋅9⋅8⋅7⋅6⋅3⋅2⋅1) and 15!=125(15⋅14⋅13⋅11⋅5⋅7⋅5)∴k=3 and h=5∴k+h=8