The sum of two numbers is 72. Their HCF and LCM are 2 and 102, respectively. The sum of the reciprocals of the same two numbers is:

Sum of two numbers = 72

HCF of the two numbers = 2

LCM of the two numbers = 102

a × b = HCF × LCM

Sum of reciprocals: $$\frac{1}{a} + \frac{1}{b} = \frac{a + b}{a \times b}$$​​

Where a is first number and b is second number. ​

Using the formula for the product of two numbers:

a × b = HCF × LCM = 2 × 102 = 204

So, a × b = 204

Now,

a + b = 72

Now, the sum of the reciprocals of the two numbers is:

​$$\frac{1}{a} + \frac{1}{b} \\ \ \\= \frac{a + b}{a \times b} \\ \ \\= \frac{72}{204}\\ \ \\= \frac{12}{34}\\ \ \\= \frac{6}{17}​$$​​

Thus, the sum of the reciprocals of the two numbers is $$\frac{6}{17}.$$​​