Find the smallest number N such that:

Question

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.

MathMate · Answer

I have one feasible solution, not sure if it is optimal. You can find others for a check along the same lines.

C=4, 3 factors: 1,2,4
B=6, 4 factors: 1,2,3,6
A=12,6 factors: 1,2,3,4,6,12
N=72,12 factors: 1,2,3,4,6,8,9,12,18,24,36,72

john · Answer

its wrong

Calvin Lin · Answer

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