Ta có :
\(\left(a,b\right).\left[a,b\right]=a.b=\left(a,b\right).60=360\)
\(\Leftrightarrow\left(a,b\right)=6\)
\(\left(a,b\right)=6\Leftrightarrow\left\{{}\begin{matrix}a=6a_1\\b=6b_2\end{matrix}\right.\) \(\left(\left(a_1;b_1\right)=1\right)\)
Lại có :
\(a.b=360\)
\(\Leftrightarrow6a_1.6b_1=360\)
\(\Leftrightarrow36.a_1.b_1=360\)
\(\Leftrightarrow a_1.b_1=10\)
Ta có bảng :
\(a\) | \(a_1\) | \(b_1\) | \(b\) | \(đk\) \(a,b\in N\) |
\(6\) | \(1\) | \(10\) | \(60\) | \(tm\) |
\(60\) | \(10\) | \(1\) |
\(6\) | \(tm\) |
\(12\) | \(2\) | \(5\) | \(30\) | \(tm\) |
\(30\) | \(5\) | \(2\) | \(12\) | \(tm\) |
Vậy ..