The list below shows the first ten numbers together with their divisors (factors):

1. $1$
2. $1$, $2$
3. $1$, $3$
4. $1$, $2$, $4$
5. $1$, $5$
6. $1$, $2$, $3$, $6$
7. $1$, $7$
8. $1$, $2$, $4$, $8$
9. $1$, $3$, $9$
10. $1$, $2$, $5$, $10$

What is the smallest number with exactly twelve divisors?

What is the smallest number with exactly fourteen divisors?