Given a list of integers, how to find the smallest positive integer such that I can get all the integers in the process of dividing it by 2?
$x_1=5, x_2=7$ is the smallest example where there is no common ancestor. Any ancestor of $x_1$ is in the range $2 \cdot 2^k + 1 \le z \le 3 \cdot 2^k - 1$, any ancestor of $x_2$ is in the range $3 \cdot 2^k + 1 \le z\le 4 \cdot 2^k - 1$. These are non-overlapping intervals with a gap of one number in between.