Question
Download Solution PDFIf the ratio of two numbers is 17 : 6 and the product of their LCM and their HCF is 102, then the sum of the reciprocals of the LCM and the HCF is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ratio of numbers = 17 : 6
LCM × HCF = 102
Formula used:
If a and b are two numbers, then a × b = LCM × HCF
Calculations
Let numbers be 17x and 6x ⇒ product = 102x²
⇒ (17x)(6x) = 102 ⇒ 102x² = 102 ⇒ x² = 1 ⇒ x = 1
⇒ Numbers = 17 and 6
⇒ HCF = 1, LCM = (17×6)/1 = 102
⇒ Required sum = \(\frac{1}{1} + \frac{1}{102} = \frac{103}{102}\)
∴ The answer is \(\frac{103}{102}\)
Last updated on Jul 17, 2025
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