If 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:

109 / 103

105 / 103

103 / 102

132 / 103

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NTPC Graduate Tier 1

2025 • 05 Jun, 2025 • Shift-3

If 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:

Correct Answer

103 / 102

[Variable Assignment]: Since the ratio of the numbers is provided as 17:6, let us establish the actual numbers as 17x and 6x, where 'x' is a common multiplier.[......

💡 Analysis & Explanation

[Variable Assignment] ▼

Since the ratio of the numbers is provided as 17:6, let us establish the actual numbers as 17x and 6x, where 'x' is a common multiplier.

[Core Arithmetical Law] ▼

A fundamental mathematical property states that the product of any two numbers is always exactly equal to the product of their HCF and LCM. Therefore, (17x) × (6x) = HCF × LCM.

[Equation Solving] ▼

Substituting the given product value, we get 102x² = 102. Dividing both sides by 102 results in x² = 1, which simply means x = 1 (since numbers are assumed positive).

[Parameter Extraction] ▼

Thus, the actual numbers are 17 and 6. For these numbers, the Highest Common Factor (HCF) is definitively 1, and the Least Common Multiple (LCM) is naturally 102.

[Final Computation] ▼

The question asks for the sum of their reciprocals: (1 / LCM) + (1 / HCF) = (1 / 102) + (1 / 1). Finding a common denominator yields (1 + 102) / 102 = 103 / 102.

Conclusion ▼

The sum evaluates to the fraction 103/102.

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If 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: