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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$10$

Vedclass · Answer

(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

Similar Questions

The smallest number which when diminished by $7,$ is divisible by $12, 16, 18, 21$ and $28$ is

Find the greatest number that will divide $964, 1238$ and $1400$ leaving remainders $41, 31$ and $51$ respectively.

The $L.C.M.$ and $G.C.D.$ of two numbers are $1530$ and $51,$ respectively. Find how many such pairs are possible?

Find the greatest number of five digits which when divided by $12, 15, 21, 25$ and $28$ leaves $5, 8, 14, 18$ and $21$ as remainders, respectively.

The $HCF$ and $LCM$ of two numbers are $21$ and $84$ respectively. If the ratio of the two numbers is $1:4$,then the larger of the two numbers is

Vedclass Test Series

Exam Paper Generator

Online Exam Module