@AndréNicolas hey , how're you?

I have entered chat. Please ask your question.

ok :)

I'm unable to get hold of relation between hcf and lcm and the numbers of which hfc and lcm are in question

@AndréNicolas E.g : you statement Since the HCF of our three numbers is 36=2^2 x 3^2, the highest power of 2 that divides n must be 2^2.

@AndréNicolas So if you have some time can teach me relation between them?

The exponent of a prime in the HCF is the MINIMUM of the exponents of $p$ in the various numbers.. The exponent of $p$ in the LCM is the MAXIMUM of the exponents of $p$ in the various given numbers.

I know the definitions but , like the question I had posted which involve both at same time , how to form relationship then?

p.s : you can delete your comments in your answer pertaining to my posted question on maths.stackexchange

So if $e$ is the exponent of $2$ in $n$, we have $\min(3,4,e)=2$ and therefore $e=2$.

If $e$ is the exponent of $3$ in $n$, then $\max(4,2,e)=5$ so $e=5$.

Hmm you were right , I believe I should post comments in your answer for clearance

The $\min$, $\max$ information is not always sufficient to determine the prime power factorization of $n$, as I mentioned in a remark at the end. But it is enough for the particular question you asked.

OK, leaving chat.

@AndréNicolas I had no offense for you in my last reply

it's just I don't get your theory interesting