HCF of 2 numbers is 24 and their LCM is 1344, if difference between the numbers is 80, find their sum.

We know that

xy= HCF *LCM

xy=24*1344=32256

Given x-y=80

Squaring,

x

^{2}+y

^{2}-2xy=6400

x

^{2}+y

^{2}-2(32256)=6400

x

^{2}+y

^{2}-64512=6400

x

^{2}+y

^{2}=70912

Now (x+y)

^{2}=x

^{2}+y

^{2}+2xy=70912+2(32256)=135424

x+y=368

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