Question

The hcf and lcm of two numbers is 13 and 455 respectively. If one of the numbers lies between 75 and 125, then that number is

Answer 1

let two numbers be x,y
=)hcf*lcm=xy
13*455=xy
5915=xy
suppose x lies between 75 and 125
x must be divisible by 13 and must be factor of 455
multiples of 13 between 75,125=78,91,108,121
among these, 91 is only factor of 455

x=91, find y by substitution of x in above equation