Question 565017
We know that 6=2*3 and 25=5*5.  Since 6 and 25 are divisors of the locker number call it x, and since 6 and 25 have no common prime factors, 2*3*5*5 must be a divisor of x.  Therefore, 1, 2, 3, 5, 5*5, 2*3, 2*5, 2*5*5, 3*5, 3*5*5, 2*3*5, 2*3*5*5 are distinct divisors of x.  But there are 12 divisors listed, so they must be the only 12 divisors of x.  So the 2*3*5*5=150 must be the locker number.