The LCM of two numbers is 495 and their HCF i | vedclass

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(A) Let the two numbers be $x$ and $y$.Given that the sum of the numbers is $x + y = 100$ $....(1)$We know that for any two numbers,the product of the

Vedclass · Accepted Answer

$10$

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(A) Let the two numbers be $x$ and $y$.Given that the sum of the numbers is $x + y = 100$ $....(1)$We know that for any two numbers,the product of the numbers is equal to the product of their $LCM$ and $HCF$.$x 	imes y = LCM 	imes HCF$$x 	imes y = 495 	imes 5 = 2475$ $....(2)$We need to find the difference,$|x - y|$.Using the algebraic identity $(x - y)^2 = (x + y)^2 - 4xy$:$(x - y)^2 = (100)^2 - 4(2475)$$(x - y)^2 = 10000 - 9900$$(x - y)^2 = 100$Taking the square root on both sides,we get:$x - y = \sqrt{100} = 10$Therefore,the difference between the two numbers is $10$.

The $LCM$ of two numbers is $495$ and their $HCF$ is $5.$ If the sum of the numbers is $100,$ then their difference is

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