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The greatest common factor and least common multiple of two numbers are 36 and 144 respectively. What is the sum of their reciprocals?

The greatest common factor and least common multiple of two numbers are 36 and 144 respectively. What is the sum of their reciprocals? Correct Answer <span class="math-tex">\(\frac{5}{144}\)</span>

Given:

HCF and LCM of 2 numbers are 36 and 144 respectively

Concept:

Product of 2 numbers is equal to their product of HCF and LCM

Co prime numbers are those numbers that have only 1 as their common factor

Calculation:

Let the numbers be 36x and 36y; (since 36 is their HCF)

⇒ 36x.36y = 36 × 144

⇒ xy = 4

The pairs possible following the condition of co-prime = (1, 4)

The numbers are 36 and 144

∴ Sum of their reciprocals = 1/36 + 1/144 = 5/144

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