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.

The numbers are 72 and 96.

Step-by-step 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.