Correct Answer - Option 2 : 52
Given:
H.C.F of numbers = 13
LCM of numbers = 585
Calculation:
Let the number be 13a and 13b where a and b are co-prime.
L.C.M of 13a and 13b = 13ab
According to question, 13ab = 585
⇒ ab = 45
⇒ ab = 5 × 9
⇒ a = 5 and b = 9 or a = 9 and b = 5
⇒ First number = 13a
⇒ First number = 13 × 5
⇒ First number = 65
⇒ Second number = 13b
⇒ Second number =13 × 9
⇒ Second number = 117
Required difference = 117 - 65 = 52
∴ Required difference = 52
