If 'a' is a natural number and HCF of a, a+5 is 5. If the LCM of the two numbers is a three-digit number, then what is the difference between the maximum & minimum possible values of the smaller number?

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Solution

The correct option is D 45
Let a =5k then a+5 =5(k+1). Both k, k +1 are co-prime.
LCM of a,a+5=5.k.(k+1)
For k =4, 5k(k+1) =100.
So minimum possible value of smaller number is 20.
Maximum value of k for which the LCM is a three digit number is 13.
Maximum possible value of the smaller number =65
So the required difference =65-20=45.

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