If the ratio of two numbers is 17 : 7 and the product of their LCM and their HCF is 119, then the sum of the reciprocals of the LCM and the HCF is:

Correct option is A

Given:

Ratio of two numbers = 17: 7

Product of their LCM and HCF = 119

Formula Used:

If numbers are ax and bx with gcd(a,b) = 1, then
HCF = x, LCM = abx, and $$\text{LCM}\times \text{HCF} = abx^2$$​​

Solution:

Let numbers be 17x and 7x ((17,7) are coprime).

Then
​$$\text{LCM}\times \text{HCF}= (119x)\times x=119x^2=119$$​​
​$$x^2=1 \implies x=1.$$​​
Hence HCF = 1, LCM = 119.

Sum of reciprocals:
​$$\frac{1}{119}+\frac{1}{1}=1+\frac{1}{119}$$​​

=$$\frac{120}{119}.$$​​
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