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Theory

    ➡ Product of two numbers = Product of their LCM and HCF

The least common multiple (LCM) is 84 times the highest common factor (HCF)

Let HCF = x => LCM = 84*x = 84x

The sum of the highest common factor and the least common multiple of two positive integers is 680

HCF + LCM = 680
=> x + 84x = 680
=> 85x = 680
=> x = \(\frac{680}{85}\) = 8

=> HCF = 8, LCM = 84 * 8 = 672

LCM * HCF = Product of the numbers

=> 672 * 8 = 56 * Other number (Given that one number is 56)
=> Other Number = \(\frac{672 * 8 }{ 56}\) = 96

So, Answer will be A.
Hope it helps!

Watch the following video to Learn the Basics of LCM and GCD

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Hello from the GMAT Club BumpBot!

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