9. (10 points) 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.
【Analysis】$667=23 \times 29$, the quotient of the least common multiple divided by the greatest common divisor is 120. If 23 is their greatest common divisor, then 29 must be split into the sum of two numbers, and their product is 120. Testing yields $29=24+5,24 \times 5=120$, so the two numbers are $24 \times 23=552,5 \times 23=115$;

Similarly, if 29 is their greatest common divisor, then 23 must be split into the sum of two numbers, and their product is 120. Testing yields $23=15+8,15 \times 8=120$; so the two numbers are $15 \times 29=435,8 \times 29=232$.

【Solution】Solution: $667=23 \times 29$, according to the problem, assuming 23 is their greatest common divisor, since $29=24+5,24 \times 5=120$,

so the two numbers are $24 \times 23=552,5 \times 23=115$;
assuming 29 is their greatest common divisor, since $23=15+8,15 \times 8=120$; so the two numbers are $15 \times 29=$ $435,8 \times 29=232$;

Answer: The two numbers are 115 and 552, or 232 and 435.