Question

The lcm of two numbers is 280 and their hcf is 8. If the sum of the number is 96 then the difference is

Answer 1

let one no. be 'x'and the other no. be 'y'.

LCM*HCF=product of the two no.s
280*8=x*y
2240=xy ____(ii)

we know,
x+y=96
x=96-y ____(i)

substituting (i) in (ii),
=>(96-y)y=2240
96y-y^2=2240
=>y^2-96y+2240=0
y^2-56y-40y+2240=0
y(y-56)-40(y-56)=0
(y-40)(y-56)=0
=>y=40(or)56

if y=40,
x+40=96
x=96-40
=56

if y=56,
x+56=96
x=96-56
=40

therefore the two no.s are 56 and 40.

the difference between the two no.s,
=>56-40=16