9. Giải:
\(\)Vì \(\left[a,b\right].\left(a,b\right)=a.b\)
\(=>a.b:\left[a,b\right]=\left(a,b\right)\)
Thay \(a.b=180\) ; \(\left[a,b\right]=60\) vào, ta có:
\(180:60=\left(a,b\right)\)
\(=>\left(a,b\right)=3\)
\(=>a=3m\) ; \(b=3n\) ; \(\left(m;n\right)=1\)
\(=>3m.3n=180\)
\(=>9.m.n=180\)
\(=>m.n=20\) ; \(\left(m,n\right)=1\)
Ta có bảng sau:
| m | 1 | 20 | 4 | 5 |
| m | 20 | 1 | 5 | 4 |
\(=>\)
| a | 3 | 60 | 12 | 15 |
| b | 60 | 3 | 15 | 12 |