Question

3) The sum and the difference of the LCM and GCD of two numbers are 312 and 264 respectively. Find the numbers if their sum is 168.

Answer 1

The numbers are 72 and 96.

Explanation:

LCM + GCF = 312

LCM - GCF = 264

2*LCM = 576

LCM = 576/2 = 288

HCF = 312–288 = 24

The product of two numbers = HCF*LCM

Let the numbers be x and (168-x)

x(168-x) = 24*288 = 6912

x^2–168x+6912 = 0

x = [168 +(168^2 -4*6912)^0.5]/2

= [168 +(28224–27648)^0.5]/2

= [168 + 576^0.5]/2

= (168+24}/2

= 192/2

= 96 and the other number is 168–96 = 72.