Question

H.C.F. of two numbers is 24 and their L.C.M is 1344. If the difference between the numbers is 80, their sum is:

Answer 1

Let the two numbers be x and y ,

HCF = 24

LCM = 1344

HCF × LCM = x×y

24×1344 = xy

xy = 32256

(x-y) = 80

x = 80+y

(80+y)×y = 32256

y^2 +80y -32256 = 0

y^2 +224y -144y -32256 = 0

y(y+224) -144(y+224) =0

y = 114 & -224

x = 80+114

x = 194

x+y = 194+80

= 274

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