A number of the form P_{1}^{a}P_{2}^{b}P_{3}^{c} will have (a + 1)(b + 1)(c + 1) factors where P_{1}, P_{2}, P_{3} are prime.
If a number has exactly 12 factors then (a + 1)(b + 1)(c + 1) should be equal to 12.
If the number has only one prime factor, it should be of the form.
P^{11} smallest no. possible = 2^{11}
If it has 2 prime factors, it can P_{1}^{3}P_{2}^{2} or P_{1}^{5}P_{2}
2^{3} x 3^{2} or 2^{5} x 3
72 or 96
If it has 3 prime factors it can be of the form
P_{1}^{a}P_{2}^{b}P_{3}^{c}
P_{1}P_{2}P_{3} = 22 x 3 x 5
P_{1}P_{2}P_{3} = 60
The smallest number possible = 60