Let n be a natural number. The HCF of n, n+10 is 10. If the LCM is x (a 2-digit number), then how many values of x are possible?

Explanation

Let the numbers be 10a and 10(a+1) where a and a+1 are coprime. Their LCM is x = 10a(a+1). Since x is a 2-digit number, testing integers for a gives x = 20 (for a=1) and x = 60 (for a=2). Thus, only two values are possible.

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