a)
[tex]\it (a,\ b) \cdot [a,\ b]=a\cdot b \Rightarrow 5\cdot [a,\ b]=3 400|_{:5} \Rightarrow [a,\ b]=680[/tex]
b)
[tex]\it a\cdot b=3400\ \ \ \ \ \ (1)\\ \\ (a,\ b)=5 \Rightarrow \begin{cases}\it a=5\cdot k\\ \\ \it b=5\cdot m\\ \\ \it (k,\ m)=1\end{cases}\ \ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow 5\cdot k\cdot5\cdot m=3400|_{:25} \Rightarrow k\cdot m=136[/tex]
[tex]\it D_{136}=\{1,\ 2,\ 4,\ 8,\ 17,\ 34,\ 68,\ 136\}\\ \\ (k,\ m) =1 \Rightarrow k\cdot m=1\cdot136=8\cdot17=17\cdot8=136\cdot1\ \ \ \ \ \ (3)\\ \\ (2),\ (3) \Rightarrow \begin{cases} \it a=5,\ \ b=680\\ \\ \it a=680,\ \ b=5\\ \\ \it a=40,\ \ b=85\\ \\ \it a=85,\ \ b=40\end{cases}[/tex]
