Notăm numărul cerut cu n.
[tex]\it n:6=a\ rest\ 3 \Rightarrow n=6a+3|_{+3} \Rightarrow n+3=6a+6 \Rightarrow n+3\in M_6\ \ \ \ \ (1)\\ \\ n:14=b\ rest\ 11 \Rightarrow n=14b+11|_{+3} \Rightarrow n+3\in M_{14}\ \ \ \ \ (2)\\ \\ n:18=c\ rest\ 15 \Rightarrow n=18c+15|_{+3} \Rightarrow n+3\in M_{18} \ \ \ \ \ (3)\\ \\ (1),\ (2),\ (3)\ \Rightarrow n+3=[6,\ \ 14,\ \ 18][/tex]
[tex]\it 6=2\cdot3\\ \\ 14=2\cdot7\\ \\ 18=2\cdot3^2\\\rule{140}{0.7}\\ \[[6,\ \ 14,\ \ 18]=2\cdot3^2\cdot7=126\\ \\ n+3=126 \Rightarrow n=126-3 \Rightarrow n=123[/tex]
