6. When the child was born, their parents were not yet 40 years old, but they were already adults. When the child turned 2 years old, the age of exactly one of the parents was divisible by 2; when the child turned 3 years old, the age of exactly one of the parents was divisible by 3, and so on. How long could such a pattern have continued?
Solution. The condition means that at the moment of the child's birth, the age of exactly one of the parents was divisible by 2, the age of exactly one of the parents - by 3, and so on (as long as this pattern continued).

Let one of the parents be 24 years old, and the other 35 years old. Then this pattern could continue until the child turned 8. Beyond that, the pattern must break. Indeed, suppose the child turned 9, and the pattern continues. Then at the moment of the child's birth, exactly one of the parents had an even number of years, exactly one - a multiple of 3, exactly one - a multiple of 6, exactly one - a multiple of 8, and exactly one - a multiple of 9. So it is the same parent, and they must be at least 72 years old, i.e., they are too old.