Divisible by $3$ $=$ $\dfrac{1000}{3} = 333$
Divisible by $7$ $=$ $\dfrac{1000}{7}= 142 $
Divisible by both $=\dfrac{1000}{\text{LCM OF 3 & 7}} = \dfrac{1000}{21} = 47 $
$n(A\cup B) = n(A) +n(B) - n(A\cap B)$
$\qquad\qquad\;= 333 + 142 - 47 = 428.$
Correct Answer: $D$