Question

# 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

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 )