Question # If ( n ) is an even natural number, then the largest natural number by which ( n(n+1)(n+2) ) is divisible is

# If ( n ) is an even natural number, then the largest natural number by which ( n(n+1)(n+2) ) is divisible is

(a) 6

(b) 8

(c) 12

(d) 24

Solution

(d) Out of ( n ) and ( n+2, ) one is divisible by 2 and the other by ( 4, ) hence ( n(n+2) ) is divisible by ( 8 . ) Also ( n, n+1 ) ( n+2 ) are three consecutive numbers, hence one of them is divisible by ( 3 . ) Hence ( n(n+1)(n+2) ) must be divisible by ( 24 . ) This will be true for any even number ( n . )