Adélka had two numbers written on a piece of paper. When she added their greatest common divisor and least common multiple, she got four different numbers, all less than 100. $S$ was amazed to find that when she divided the largest of these four numbers by the smallest, she got the greatest common divisor of all four numbers.

Which numbers did Adélka have written on the paper?

(M. Petrová)

Hint. What is the relationship between the least common multiple and the greatest common divisor of two numbers?
All four numbers were distinct, so the original two numbers were distinct, their greatest common divisor was less than each of these numbers, and their least common multiple was greater than each of these numbers. If we denote the greatest common divisor by $d$, we can write the original two numbers as $d \cdot x$ and $d \cdot y$, where $x10$,
- etc.

Adélka had written the numbers $6 \cdot 2=12$ and $6 \cdot 3=18$, to which she later added 6 and $6 \cdot 6=36$.

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