Find the smallest number N such that:
The number of divisors of N is A.
The number of divisors of A is B.
The number of divisors of B is C.
The number of divisors of C is 3.
Details and assumptions
The divisors include and the number itself. For example, the number of divisors of is .
You may read Divisors of an Integer to learn how to count the number of divisors of a given integer.