30

Number
$30$ (thirty) is:


 * $2 \times 3 \times 5$


 * The $3$rd primorial, after $1, 2, 6$ (counting $1$ as the zeroth):
 * $30 = 5\# = 2 \times 3 \times 5$
 * Hence the smallestpositive integer with $3$ distinct prime factors.