Determine the number of integers $n$ such that $1 \leqslant n \leqslant 10^{10}$, and such that for all $k=1,2, \ldots, 10$, the integer $n$ is divisible by $k$.
Answer: 3968253. $n$ must be divisible by $2^{3} \times 3^{2} \times 5 \times 7=2520$, so the answer is the integer part of $10^{10} / 2520$.