Smallest Number with 16 Divisors

Theorem
The smallest positive integer with $16$ divisors is $120$.

Proof
From Tau Function of 120:
 * $\map \tau {120} = 16$

The result is a specific instance of Smallest Number with $2^n$ Divisors:


 * $120 = 2 \times 3 \times 4 \times 5$