Gọi số đó là a ( a∈N*)
Ta có:
\(\left\{{}\begin{matrix}a=3x+1\\a=4y+2\\a=5z+3\\a=6t+4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a+62=3x+63=3\left(x+21\right)\\a+62=4y+64=4\left(y+16\right)\\a+62=5z+65=5\left(z+13\right)\\a+62=6t+66=6\left(t+11\right)\end{matrix}\right.\Rightarrow\left(a+62\right)⋮3,4,5,6\Rightarrow\left(a+62\right)⋮ƯCLN\left(3;4;5;6\right)\Rightarrow\left(a+62\right)⋮60\)\(\Rightarrow a+62\in\left\{120;180;240;300;360;420;480;540;600;660;...\right\}\Rightarrow a\in\left\{58;118;178;238;298;358;418;478;538;598;...\right\}\)Mà \(a⋮11\)⇒a nhỏ nhất bằng 418
Vậy \(a=418\)thỏa mãn đề ra
