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When the square of the difference of two natural numbers is subtracted from the square of the sum of the same two numbers and the result is divided by four, we get
Lets assume both the natural numbers as {a,b} , then manipulative calculation is :
$$\dfrac{(a+b)\ ^2-\left(a-b\right)^2\ }{4}\ =\ ab$$
The final obtained value is "ab" i.e product of both natural numbers .
We know that, always the property of HCF, LCM :
LCM{a,b} x HCF{a,b} = a x b = Product of the given two numbers.
Therefore 'ab' = product of LCM and HCF .
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