HCF $\times$ LCM = product of the two numbers

How to use it

1. 1When three of the four quantities are known, solve for the fourth.
2. 2If $\text{HCF}(a,b)=1$ then $\text{LCM}(a,b)=ab$.
3. 3Combine with '$\text{HCF}$ divides both numbers' to pin down candidate pairs.

Step-by-step

1. 1
   $6\times 36=12\times n$

   Why: Apply the identity with the three known quantities.

2. 2
   $216=12n\Rightarrow n=18$