Number of Divisors

Number Theory Level 4

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 $1$ and the number itself. For example, the number of divisors of $10$ is $4$ .

You may read Divisors of an Integer to learn how to count the number of divisors of a given integer.