energetics
Thanks Ian, that clears it up.
If it was worded "the least common denominator of the product of x/y and 1/3 is 6" then it would be solved as I wrote above?
That sentence wouldn't mean anything - it would be like saying "the least common multiple of 6 is 6". If you are talking about the "least
common multiple", you are talking about a multiple that is common to two (or more) numbers. In the same way, if you talk about a least common denominator, you are talking about a denominator common to two or more fractions. In your sentence, you're only talking about the denominator of a single fraction, the product of the fractions you mention.
But I think I may now understand how you're interpreting the wording. I think you're interpreting it to mean something like "the lowest possible denominator (if everything stays an integer) of the product of x/y and 1/3 is 6", or "if (x/y)(1/3) were completely reduced, its denominator would be 6". But if that's what the question meant, they would need to use different phrasing - they would need to talk about reducing that fraction completely, and not about "least common denominators".