For all integral values of n, the largest number that exactly divides each number of the sequence \[(n-1)n(n+1),\] \[n(n+1)(n+2),\] \[(n+1)(n+2)(n+3),...\] is
A) 12
B) 6
C) 3
D) 2
Correct Answer:
D
Solution :
The largest number will be 6. For \[n=2\] \[(n-1)n(n+1)=6,\] For \[n=3,\] \[(n-1)(n)(n+1)=24\,etc.\]