Gọi \(ƯCLN\left(a,b\right)=d\Rightarrow\left\{{}\begin{matrix}a=d.a_1\\b=d.b_1\\ƯCLN\left(a_1;b_1\right)=1\end{matrix}\right.\)
\(\Rightarrow BCNN\left(a,b\right)=d.a_1.b_1=140\)\(\left(1\right)\)
Mà \(\dfrac{a}{b}=\dfrac{4}{5}\Rightarrow\dfrac{d.a_1}{d.b_1}=\dfrac{4}{5}\Rightarrow\dfrac{a_1}{b_1}=\dfrac{4}{5}\) \(\Rightarrow\left[{}\begin{matrix}a_1=4\\b_1=5\end{matrix}\right.\) (do \(ƯCLN\left(a_1,b_1\right)=1\))\(\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Rightarrow d.4.5=140\)
\(\Rightarrow d=7\)
\(\Rightarrow\left[{}\begin{matrix}a=7.4=28\\b=7.5=35\end{matrix}\right.\) (thỏa mãn)
Vậy \(2\) số \(a,b\) cần tìm là \(28,35\)
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