$S = \{1,2,3,\ldots,6300\}$ Let A: Set of integers divisible by 3, B: Set of integers divisible by 5, C: Set of integers divisible by 7.
We are to find: $n(S) - n(A \cup B \cup C) = n(S) - [n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(A \cap C) + n(A \cap B \cap C)]$
$= 6300 - \left\{\left[\frac{6300}{3}\right] + \left[\frac{6300}{5}\right] + \left[\frac{6300}{7}\right] - \left[\frac{6300}{3\times5}\right] - \left[\frac{6300}{5\times7}\right] - \left[\frac{6300}{3\times7}\right] + \left[\frac{6300}{3\times5\times7}\right]\right\}$
i.e., $n(A \cup B \cup C)^c = 2880$.