Question 125
Consider the $m \times n$ table, $m, n \ge 2$ ($m$ rows are enumerated $1, 2, \ldots, m$ and $n$ columns are enumerated $1, 2, \ldots, n$), which is filled with positive integers. Let $b_i$ be the $lcm$ (least common multiple) of all numbers in the $i^{th}$ row, $1 \le i \le m$, and let $B$ be the $gcd$ (greatest common divisor) of numbers $(b_1, b_2, \ldots, b_m)$. Also, let $c_j$ be the $gcd$ of all numbers in $j^{th}$ column, $1 \le j \le n$, and let $C$ be the $lcm$ of numbers $(c_1, c_2, \ldots, c_n)$. Is it true that $B$ is divisible by $C$, or is $C$ divisible by $B$?