Find a possible pair of numbers given HCF and a factor of the LCM I was just going through a GCSE paper with a student and I came across a question that I'm struggling to find a good method for. The question was this:


  Martin thinks of two numbers.
  
  The Highest Common Factor of the two numbers is 6   The Lowest Common
  Multiple is a multiple of 15
  
  Write a pair of numbers that Martin could be thinking of.


It took me an embarrassingly long time to come up with a solution but I still don't have a method that will work quickly for different numbers. What would be the best way to come up with a solution?
Both numbes must be multiples of $6$ and at least one must be a multiple of $5$ (because $5$ is a prime dividing $15$). So the first attempt is $a=30$ and $b=6$ and works
this question is incorrect!

To have an LCM of 15 the numbers can only be 1 and 15 or 3 and 5

The given answer of 6 and 30 would give a HCF of 6 and and LCM of 30