Both the H.C.F and the difference of two numbers is 7. If the L.C.M of the two numbers is a three digit number, then what is the maximum possible value of the smaller number?

Options:

A . 77

B . 84

C . 70

D . 63

Answer: Option A : A Let the smaller number be 7x, then the larger number will be (7x+7) = 7(x+1) Since x and (x+1) are co-prime, the LCM would be 7×x×(x+1). Maximum value of x such that LCM is a three digit number is x=11. So, smaller number = 77.

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