Using HCF–LCM product with a sum constraint: The HCF and LCM of two numbers m and n are 6 and 210, respectively. If m + n = 72, find the value of 1/m + 1/n.

Introduction / Context:
This question combines the product identity for two numbers with a sum constraint to compute the sum of reciprocals directly. It illustrates how HCF and LCM can determine mn, and with m + n given, one can form (m + n)/(mn) without solving for m and n individually.

Given Data / Assumptions:

• HCF(m, n) = 6
• LCM(m, n) = 210
• m + n = 72
• Find 1/m + 1/n.

Concept / Approach:
Use the identity m * n = HCF * LCM. Then 1/m + 1/n = (m + n) / (m * n). This bypasses the need to find m and n separately and leverages given aggregate information efficiently.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 1/35, 3/35, 5/37 do not equal 72/1260 after reduction and thus contradict the computed ratio.

Common Pitfalls:

• Miscalculating mn or simplifying 72/1260 incorrectly.

Final Answer: