Question

If $L.C.M.$ of two numbers is $180,H.C.F.$ is $15$ and sum of them is $105$, what is the difference between those two numbers ?

Answer 1

$LCM\times HCF=x\times y$.............Equation 1

Now, we have given that $LCM=180$ AND $HCF=15$

Solving the equation 1 we will get

$xy=180\times 15=2700$.......Equation 2

Now, $(x-y{)}^2=x^2+y^2-2xy$

Solving this we will get, $x-y=\sqrt{255}=15$

Hence the difference between the given two numbers is $15$.