Giải:
Gọi 3 số đó là a; b; c.
Theo bài ra ta có:
\(\dfrac{a}{b}=\dfrac{5}{9}\Rightarrow\dfrac{a}{5}=\dfrac{b}{9}\Rightarrow\dfrac{a}{10}=\dfrac{b}{18}.\)
\(\dfrac{a}{c}=\dfrac{10}{7}\Rightarrow\dfrac{a}{10}=\dfrac{c}{7}.\)
\(\Rightarrow\dfrac{a}{10}=\dfrac{b}{18}=\dfrac{c}{7}.\)
Đặt \(\dfrac{a}{10}=\dfrac{b}{18}=\dfrac{c}{7}=k\Rightarrow a=10k;b=18k;c=7k.\)
Ta có:
\(BCNN_{\left(a;b;c\right)}=3150.\)
\(\Rightarrow BCNN_{\left(10k;18k;7k\right)}=3150.\)
\(\Rightarrow kBCNN_{\left(10;18;7\right)}=3150.\)
Mà \(BCNN_{\left(10;18;7\right)}=630.\)
\(\Rightarrow k.630=3150.\)
\(\Rightarrow k=5.\)
Từ đó: \(\left\{{}\begin{matrix}a=5.10=50.\\b=5.18=90.\\c=5.7=35.\end{matrix}\right.\)
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