Question
Download Solution PDFIf the ratio of two numbers is 5 : 3 and the product of their LCM and their HCF is 135, then the sum of the reciprocals of the LCM and the HCF is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ratio of two numbers = 5:3
Product of LCM and HCF = 135
Formula used:
LCM × HCF = Product of the numbers
Calculation:
Numbers = 5x and 3x
Product of numbers = 5x × 3x = 15x2
⇒ LCM × HCF = 15x2 = 135
⇒ x2 = 135/15
⇒ x2 = 9
⇒ x = 3
Numbers = 5x = 15, and 3x = 9
LCM of 15 and 9 = 45
HCF of 15 and 9 = 3
Sum of reciprocals of LCM and HCF = (1/LCM) + (1/HCF)
⇒ Sum = (1/45) + (1/3)
⇒ Sum = 16/45
∴ The correct answer is option (3).
Last updated on Jul 17, 2025
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