A person distributes pens among A, B, C, and D in the ratio 1/3 : 1/4 : 1/5 : 1/6. What is the minimum total number of pens so that each gets a whole number of pens?

Introduction / Context: When shares are proportional to fractions, choose a common parameter so each share becomes an integer. The least such total comes from using the least common multiple of denominators.

Given Data / Assumptions: Shares ∝ 1/3, 1/4, 1/5, 1/6.

Concept / Approach: Let each share be k times the respective fraction. To make shares integers, pick k as LCM of the denominators. Then sum the integer shares for the minimum total.

Step-by-Step Solution: LCM(3, 4, 5, 6) = 60. Shares: 60*(1/3) = 20; 60*(1/4) = 15; 60*(1/5) = 12; 60*(1/6) = 10. Minimum total pens = 20 + 15 + 12 + 10 = 57.

Verification / Alternative check: Any smaller scaling will yield a non-integer for at least one recipient because 60 is the least common multiple.

Why Other Options Are Wrong: 45, 65, 75, 60 are not the minimal achievable integer-sum with integral shares under the given proportions.

Common Pitfalls: Adding fractions directly or failing to use LCM to clear denominators.

Final Answer: 57