Let the three consecutive positive integers are: n, (n+1)and (n+2)

Product = n*(n+1)* (n+2)

Let n=1

product = 1*(1+1)* (1+2)

            = 1*2*3

            = 6

So, the product is divisible by 6

Again let n=2

product = 2*(2+1)* (2+2)

            = 2*3*4

            = 24

So, the product is divisible by 6

Again let n=3

product = 3*(3+1)* (3+2)

            = 3*4*5

            = 60

So, the product is divisible by 6

Hence, the product of three consecutive positive integers is always divisible by 6.