a) \(24=2^3.3\)
\(60=2^2.3.5\)
\(UCLN\left(a;b\right)=UCLN\left(24;60\right)=2^2.3=6\)
\(BCNN\left(a;b\right)=BCNN\left(24;60\right)=2^3.3.5=120\)
\(a.b=UCLN\left(a;b\right).BCNN\left(a;b\right)\)
\(\Rightarrow a.b=6.120=720\)
mà \(\dfrac{a}{b}=\dfrac{24}{60}\Rightarrow\dfrac{a}{24}=\dfrac{b}{60}=\dfrac{720}{24.60}=\dfrac{1}{2}\)
\(\Rightarrow\left\{{}\begin{matrix}a=24.\dfrac{1}{2}=12\\b=60.\dfrac{1}{2}=30\end{matrix}\right.\)
Vậy Phân số cần tìm là \(\dfrac{12}{30}\)
b) \(\left\{{}\begin{matrix}14=2.7\\21=3.7\end{matrix}\right.\)
\(\Rightarrow UCLN\left(a;b\right)=UCLN\left(14;21\right)=7\)
\(a.b=UCLN\left(14;21\right).BCNN\left(14;21\right)\)
\(\Rightarrow a.b=7.3456=24192\)
\(\dfrac{a}{b}=\dfrac{14}{21}\Rightarrow\dfrac{a}{14}=\dfrac{b}{21}=\dfrac{a.b}{14.21}=\dfrac{24192}{294}=\dfrac{576}{7}\)
\(\Rightarrow\left\{{}\begin{matrix}a=\dfrac{576}{7}.14=1152\\b=\dfrac{576}{7}.21=1728\end{matrix}\right.\)
Vậy phân số cần tìm là \(\dfrac{1152}{1728}\)
