Question 7
II 1 (POL 2)
Let $a_i,b_i$ be coprime positive integers for $i=1,2,\ldots,k$, and $m$ the least common multiple of $b_1,\ldots,b_k$. Prove that the greatest common divisor of $a_1\frac m{b_1},\ldots,a_k\frac m{b_k}$ equals the greatest common divisor of $a_1,\ldots,a_k$.
Let $a_i,b_i$ be coprime positive integers for $i=1,2,\ldots,k$, and $m$ the least common multiple of $b_1,\ldots,b_k$. Prove that the greatest common divisor of $a_1\frac m{b_1},\ldots,a_k\frac m{b_k}$ equals the greatest common divisor of $a_1,\ldots,a_k$.