1.
[tex]\it a\cdot b=(a,\ b)\cdot\[[a,\ b]=10\cdot60=600\ \ \ \ \ (1)\\ \\ \\ (a,\ b)=10 \Rightarrow \begin{cases} \it a=10x\\ \\ \it b=10y\\ \\ \it (x,\ y)=1\end{cases}\ \ \ \ \ (2)[/tex]
[tex]\it (1), (2) \Rightarrow 10x\cdot10y=600|_{:100} \Rightarrow x\cdot y=1\cdot6=2\cdot3=3\cdot2=6\cdot1\ \ \ \ (3)\\ \\ (2),\ (3) \Rightarrow \begin{cases}\it a=10\cdot1=10;\ \ b=10\cdot6=60\\ \\ \it a=10\cdot2=20;\ \ b=10\cdot3=30\\ \\ \it a=10\cdot3=30;\ \ b=10\cdot2=20\\ \\\it a=10\cdot6=60;\ \ b=10\cdot1=10 \end{cases}[/tex]
2.
Notăm numărul cerut cu n.
[tex]\it n-13\in M_{14}\cap M_{21}\cap M_{28}\\ \\ 4=2\cdot7\\ \\ 21=3\cdot7\\ \\ 28=4\cdot7\\\rule{110}{0.6}\\\[[14,\ 21,\ 28]=2\cdot3\cdot4\cdot7=168\\ \\ n-13=168|_{+13}\Rightarrow n=181[/tex]
