15. (2001 China National Team Selection Test for IMO) Given an integer $n$ greater than 3, let real numbers $x_{1}, x_{2}, \cdots, x_{n}, x_{n+1}, x_{n+2}$ satisfy the condition
$0<x_{1}<x_{2}<\cdots<x_{n}<x_{n+1}<x_{n+2}$.
Find the minimum value of $\frac{\left(\sum_{i=1}^{n} \frac{x_{i+1}}{x_{i}}\right)\left(\sum_{j=1}^{n} \frac{x_{j+2}}{x_{j+1}}\right)}{\left(\sum_{k=1}^{n} \frac{x_{k+1} x_{k+2}}{x_{k+1}^{2}+x_{k} x_{k+2}}\right)\left(\sum_{i=1}^{n} \frac{x_{l+1}^{2}+x_{l} x_{l+2}}{x_{l} x_{l+1}}\right)}$
and determine all real number sequences $x_{1}, x_{2}, \cdots, x_{n}, x_{n+1}, x_{n+2}$ that achieve this minimum value.