Question

the sum and the difference of the LCM and the HCF of two numbers is 312 and 264 respectively. find the numbers if there sum is 168

Answer 1

Step-by-step explanation:

LCM + HCF = 312

LCM - HCF = 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.

The numbers are 72 and 96.

Check: 72 = 2x2x2x3x3

96 = 2x2x2x2x2x3

HCF = 2x2x2x3 = 24 and LCM = 2x2x2x2x2x3x3 = 288.

Sum of HCF + LCM = 24+288 = 312

LCM - HCF = 288–24 = 264.

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