Question

If the sum of two numbers is 20 and their hcf and lcm are 1 and 91

Answer 1

HCF × LCM = 91
= product of the two numbers
let the numbers to be x and y
so, x×y= 91
= y= 91/x
we have x+y=20
= x+91/x= 20
= x^2-20x+91=0
= x2-13x-7x+91=0
=x(x-13)-7(x-13)= 0
=(x-13)(x-7)=0
so, x= 13 or x=7
when x=13 then y= 7
when x=7 then y=13
so the numbers are 13 and 7