The G.C.D of two numbers is $23$. $13$ and $14$ are also factors of the L.C.M [out of some unknown number of factors]. What is the larger number?
The thing I am able to infer is that both numbers are divisible by $23$. Then this means that their L.C.M is divisible by all $23$, $13$ and $14$. So, may I assume that the L.C.M is just $23 \cdot 13 \cdot 14$? And if so, how?
Please show me how to go about the rest of the question.
UPDATE $\ \ \ \ $I found some assistance from a friend outside M.SE and his answer was correct: The two numbers are $23 \cdot 13$ and $23 \cdot 14$.
This question is from the previous year's papers of a competitive exam. Also, if possible, please retag the question accordingly.