\(a.b=4500\left\{\begin{matrix}BCNN\left(a;b\right)=300\\UCLN\left(a;b\right)=15\end{matrix}\right.\)
\(UCLN\left(a;b\right)=15\Rightarrow\left\{\begin{matrix}a=15.m\\b=15.n\end{matrix}\right.\)
\(\)( \(m;n\in\) N*, \(UCLN\left(m;n\right)=1,\left(m< n\right)\))
\(a.b=4500\)
\(\Leftrightarrow15.m.15.n=4500\)
\(\Leftrightarrow m.n=4500:\left(15.15\right)\)
\(\Leftrightarrow m.n=20\)
\(m\) | \(1\) | \(4\) |
\(n\) | \(20\) | \(5\) |
\(a\) | \(15\) | \(60\) |
\(b\) | \(300\) | \(75\) |
Vì \(a+15=b\) nên \(a=60\) và \(b=75\)