Question

BCNN(a,b)=630,,UCLN(a,b)=18.Tìm 2 số a, b

Answer 1

Ta có:

\(ab=630.18=11340\)

Đặt \(a=18m;b=18n\) (Vì \(ƯCLN\left(a;b\right)=18\))

Vì \(a>b;m>n\)

\(\Rightarrow18m.18n=11340\)

\(\Rightarrow18.18.m.n=11340\)

\(\Rightarrow340.m.n=11340\)

\(\Rightarrow mn=11340\div324\)

\(\Rightarrow mn=35=7.5=35.1\)

\(\Rightarrow\left[\begin{matrix}m=7;n=5\\m=35;n=1\end{matrix}\right.\Rightarrow\left[\begin{matrix}a=18m=126;b=18n=90\\a=18m=630;b=18n=18\end{matrix}\right.\)

Vì \(a\) \(⋮̸\) \(b\Rightarrow a=126;b=90\)

Vậy \(a=126;b=90\)