If the $x_i$ are rational, take the lcm of the denominators and decrease it by $1$.

If they are not necessarily rational, act similarly: take a $k$ such that all the $kx_i$ are sufficiently close to integers, and decrease that $k$ by $1$.

If the $x_i$ are rational, take the lcm of the denominators and decrease it by $1$.

If they are not necessarily rational, act similarly: using, e.g., Kronecker's theorem, take a $k$ such that all the $kx_i$ are sufficiently close to integers, and decrease that $k$ by $1$.