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

Seema,Meena,and Reena start jogging around a circular stadium and complete one round in $54 \text{ seconds}$,$42 \text{ seconds}$,and $63 \text{ seconds}$ respectively. Approximately after how many minutes will they meet again at the starting point?

Find the greatest number that will divide $390, 495,$ and $300$ without leaving a remainder.

Find the greatest number of five digits which becomes exactly divisible by $10, 12, 15$ and $18$ when $3769$ is added to it.

Philip, Tom, and Brad start jogging around a circular field and complete a single round in $18\, \text{seconds}$, $22\, \text{seconds}$, and $30\, \text{seconds}$, respectively. In how much time will they meet again at the starting point?

Find the maximum possible length which can be used to measure exactly the lengths $6 \, m$,$4 \, m \, 75 \, cm$,and $10 \, m \, 25 \, cm$. (in $, cm$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module