What is the smallest of the eight natural numbers with different divisors?

What is the smallest of the eight natural numbers with different divisors?

The number of divisors is equal to the product of prime factor times plus 1
8= (1+1)(1+1)(1+1) = (1+1)(3+1) = (7+1)
So the form of n is p * Q * r, or p * q ^ 3, or P ^ 7
The minimum numbers corresponding to the above forms are:
2*3*5 = 30
2^3 * 3 = 24
2^7 = 128
So the smallest number is 24