210

Number
$210$ (two hundred and ten) is:


 * $2 \times 3 \times 5 \times 7$


 * The $4$th primorial, after $1, 2, 6, 30$ (counting $1$ as the zeroth):
 * $210 = 7 \# = 2 \times 3 \times 5 \times 7$
 * Hence the smallest positive integer with $4$ distinct prime factors.