If the ratio of two numbers is 4:3 and the product of their LCM and their HCF is 432 , then the sum of the reciprocals of the LCM and the HCF is:

Correct option is A

Given: ​

Ratio of two numbers = 4 : 3 

Product of LCM and HCF = 432 

Concept Used: ​

Product of two number = HCF $$\times$$ LCM

Solution: ​

Let the number be 4x and 3x 

So, 

​$$4x \times 3x = 432 \\ \ \\ 12x^2= 432 \\ \ \\ \implies x^2 = \frac{432}{12} = 36 \\ \ \\ x =6$$

Numbers be  24 and 18 

thus, HCF is 6 and LCM is 72 

Sum of Reciprocal of HCF and LCM 

$$=\frac{1}{6}+\frac{1}{72} \\ \ \\ = \frac{12 + 1}{72} \\ \ \\ = \frac{13}{72}$$​