Given a real number x, let \lfloor x\rfloor denote the greatest integer less than or equal to x. For a certain integer k, there are exactly 70 positive integers n_{1}, n_{2}, \ldots, n_{70} such that k=\left\lfloor\sqrt[3] {n_{1}}\right\rfloor=\left\lfloor\sqrt[3]{n_{2}}\right\rfloor=\cdots=\left\lfloor\sqrt[3]{n_{70}}\right\rfloor and k divides n_{i} for all i such that 1 \leq i \leq 70. Find the maximum value of \frac{n_{i}}{k} for 1 \leq i \leq 70.