Question

L.c.m.of two numbers is 180 ,h.c.f is 15 andsum of them is105 ,what is the difference between those two numbers

Answer 1

Let the two numbers be x and y.

To solve this question, we will make use of a very important property of LCM and HCF. This is as shown below:

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

Now, it is given that LCM=180 and HCF=15

Thus, Equation 1 will give us:

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

Now, we know that: $(x-y)^2=x^2+y^2-2xy$

This can be rewritten as: $(x-y)^2=(x+y)^2-2xy-2xy=(x+y)^2-4xy$

Therefore, $(x-y)^2=105^2-4\times 2700=225$

Thus, $x-y=\sqrt{225}=15$

And hence  the difference between the given two numbers is 15.

Answer 2

LCM * HCF = x * y .............Equation 1

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

Solving the equation 1 we will get

xy = 180 * 15 = 2700.......Equation 2

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

Solving this we will get, x - y = under root 255 = 15

Hence the difference between the given two numbers is 15.