Tìm các số tự nhiên \(x\), sao cho

h) \(x\,\, \vdots \,\,{\rm{12,}}\,\,x\,\, \vdots \,\,{\rm{21,}}\,\,x\,\, \vdots \,\,{\rm{28}}\) và \(150 < x < 200\).

h) Vì \(x\,\, \vdots \,\,{\rm{12,}}\,\,x\,\, \vdots \,\,{\rm{21,}}\,\,x\,\, \vdots \,\,{\rm{28}}\) nên \(x \in {\rm{BC}}\left( {12,\,\,21,\,\,28} \right)\).

Ta có: \(12 = {2^2} \cdot 3;\,\,\,\,\,21 = 3 \cdot 7;\,\,\,\,\,28 = {2^2} \cdot 7.\)

Do đó \(BCNN\left( {12,\,\,21,\,\,28} \right) = {2^2} \cdot 3 \cdot 7 = 84\).

Suy ra \({\rm{BC}}\left( {12,\,\,21,\,\,28} \right) = {\rm{B}}\left( {84} \right) = \left\{ {0;\,\,84;\,\,168;\,\,252;\,\,336;\,\,...} \right\}\).

Mà \(150 < x < 200\) nên \(x = \,168\).

 Vậy \(x = \,168\).