An ordinary GCF question can be started the moment it is read. This one cannot: you are given the greatest common factor, the least common multiple and a range, and no one of those three facts is enough on its own. The arithmetic is the same arithmetic — what changes is that there is something to work out before you can begin.
The answer key prints on a separate page.
Running the question backwards is what makes it a puzzle. Both numbers must be multiples of the GCF, so they are GCF×m and GCF×n; their least common multiple is GCF×m×n, so m and n multiply to LCM ÷ GCF; and m and n can share no factor, or the GCF would have been bigger than the one you were given. That last clause is the whole idea, and it is the step a child has to find rather than recall.
The trap is measured rather than decorated. The pair (GCF, LCM) itself always satisfies both headline facts — the GCF of 5 and 30 really is 5, and their LCM really is 30 — so a reader who treats the range as decoration writes down an answer that is wrong for a reason worth discussing. Every question on the sheet has that trap in it, and the range is always what rules it out.