Question

Tìm a,b,c biết \(\frac{a}{b}=\frac{3}{5}\), \(\frac{a}{c}=\frac{7}{4}\) và BCNN(a,b,c)=1260

Answer 1

\(\frac{a}{b}=\frac{3}{5}\Leftrightarrow\frac{a}{3}=\frac{b}{5}\Leftrightarrow\frac{a}{21}=\frac{b}{35}\)

\(\frac{a}{c}=\frac{7}{4}\Leftrightarrow\frac{a}{7}=\frac{c}{4}\Leftrightarrow\frac{a}{21}=\frac{c}{12}\)

<=>\(\frac{a}{21}=\frac{b}{35}=\frac{c}{12}\)

Đặt \(\frac{a}{21}=\frac{b}{35}=\frac{c}{12}=k\Rightarrow\hept{\begin{cases}a=21k\\b=35k\\c=12k\end{cases}}\)

=>\(BCNN\left(a;b;c\right)=BCNN\left(21k;35k;12k\right)=420k=1260\)

=> k = 1260 : 420 = 3

=>\(\hept{\begin{cases}a=21.3=63\\b=35.3=105\\c=12.3=36\end{cases}}\)

Vậy ..............