[tex]\it Fie\ n\ num\breve arul\ cerut.\\ \\ n:12=a\ \ rest\ \ 11 \Rightarrow n=12\cdot a+11 \Rightarrow n-11=12\cdot a \Rightarrow n-11\in M_{12}\\ \\ n:16=b\ \ rest\ \ 11 \Rightarrow n=16\cdot b+11 \Rightarrow n-11=16\cdot b \Rightarrow n-11\in M_{16}\\ \\ n:18=c\ \ rest\ \ 11 \Rightarrow n=18\cdot c+11 \Rightarrow n-11=18\cdot c \Rightarrow n-11\in M_{18}[/tex]
Determinăm cel mai mic multiplu comun al numerelor 12, 16 și 18.
[tex]\it 12=2^2\cdot3\\ \\16=2^4\\ \\18=2\cdot3^2\\ ------\\\Big [ 12,\ 16,\ 18 \Big]=2^4\cdot3^2=16\cdot9=144 \Rightarrow n-11=144|_{+11} \Rightarrow n=133[/tex]
