9. The sum of two natural numbers is 667, and the quotient of their least common multiple divided by their greatest common divisor is 120. Find these two numbers.
【Answer】115,552 or 232,435.
We get $\left\{\begin{array}{l}m(x+y)=667 \\ \frac{m x y}{m}=x y=120\end{array},\left\{\begin{array}{l}m(x+y)=667=23 \times 29 \\ x y=120\end{array}, x, y\right.\right.$ are coprime.
So $120=1 \times 120=2 \times 60=3 \times 40=5 \times 24=8 \times 15$
The solutions that meet the requirements are $\left\{\begin{array}{l}x+y=24+5=29 \\ m=23\end{array}\right.$ or $\left\{\begin{array}{l}x+y=8+15=23 \\ m=29\end{array}\right.$
The corresponding numbers are 115,552 or 232,435.