Correct Answer - Option 1 :
\(\dfrac{11}{160}\)
Given:
HCF = 15
LCM = 480
Formula used:
HCF × LCM = a × b
Calculation:
Let the number be 15a and 15b
15a × 15b = 15 × 480
⇒ ab = 7200/225
⇒ ab = 32
Now we will check for co-prime factors for the 32
(1, 32) (2, 16) and (4, 8)
There is only one pair (1, 32) which is co-prime
So the number will be
15a = 15 × 1 = 15
15b = 15 × 32 = 480
Sum of their reciprocal
\(\dfrac{1}{15} \ + \ \dfrac{1}{480} = \dfrac{32 \ + \ 1 }{480}\)
⇒ \(\dfrac{33}{480} = \dfrac{11}{160}\)
∴ The sum of their reciprocal is \(\frac{11}{160}\)