73 (1193). The least common multiple of two numbers, neither of which divides the other, is 90, and their greatest common divisor is 6. Find these numbers.
Solution. Knowing the rule for finding the LCM and GCD of numbers using their prime factorization, it is easy to find the solution method:

1) Represent the LCM - the number 90 - as a product of prime factors: $90=2 \cdot 3 \cdot 3 \cdot 5$.
2) Since the GCD of the sought numbers is 6, and they do not divide each other (neither of the numbers is equal to 6), then one of them is $6 \cdot 3=18$, the other is $-6 \cdot 5=30$.

Answer: 18 and 30.