Two bells ring at intervals of 63 seconds and 74 seconds. If they both ring at 10 O'clock in the morning together, after how many seconds will they ring together again?

1. A

   4482

2. B

   4662

3. C

   4552

4. D

   4772

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-3rd)

Explanation

• The problem asks for the next time two events, occurring at different regular intervals, will happen simultaneously. This requires finding the Least Common Multiple (LCM) of the intervals.
• The intervals for the two bells are 63 seconds and 74 seconds.
• To find the LCM, we can use prime factorization. The prime factors of 63 are 3 × 3 × 7.
• The prime factors of 74 are 2 × 37.
• Since the numbers 63 and 74 have no common prime factors (they are coprime), their LCM is simply their product.
• Calculation: 63 × 74 = 4662. Thus, they will ring together again after 4662 seconds.

Why Other Options Were Wrong

• Option A: This is an incorrect result of the multiplication. It may arise from a calculation error, such as multiplying 63 by an incorrect number like 71 or 72.
• Option C: This is a result of a calculation error. It is not the product of 63 and 74.
• Option D: This is an incorrect product of 63 and 74, likely due to a mistake during manual multiplication.

Related Visual

• Visual 1: Infographic: A step-by-step guide on how to find the Least Common Multiple (LCM) of two numbers using the prime factorization method.
• Visual 2: Flowchart: A decision-making flowchart that starts with 'Do the numbers have common factors?' and leads to the correct method for finding the LCM (either by listing multiples or by prime factorization).

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of Least Common Multiple (LCM) for a practical problem as background academic context rather than a clinical decision trigger.
• This is a general aptitude question designed to test mathematical reasoning and calculation skills, which are foundational for nurses.
• While LCM itself is not a common daily calculation in nursing, the underlying skill of precise mathematical computation is critical for tasks like medication dosage calculation, IV drip rate adjustment, and interpreting patient data charts.
• What if the intervals were 60 seconds and 75 seconds? The prime factors of 60 are 2² × 3 × 5, and for 75 are 3 × 5². The common factors are 3 and 5. The LCM would be 2² × 3¹ × 5² = 4 × 3 × 25 = 300 seconds. The answer would change because the numbers are not coprime.

How to Approach the Question

• First, read the question carefully to understand what is being asked. The keywords are 'ring together again', which points to a recurring event.
• Recognize that this is a problem about finding a common point in time for two different cycles. This is a classic application of the Least Common Multiple (LCM).
• Identify the two intervals given in the problem: 63 seconds and 74 seconds.
• Determine the best method to find the LCM of 63 and 74. Prime factorization is a reliable method.
• Find the prime factors of 63 (3 × 3 × 7) and 74 (2 × 37).
• Check if there are any common prime factors. In this case, there are none.

Concept Tested & Keywords

• Concept Tested: Calculation of Least Common Multiple (LCM) for a practical problem.
• Stem keywords: bells, intervals, 63 seconds, 74 seconds, ring together
• Lead-in keywords: after how many seconds

Question ID

QEAxeOMu_9vb0QKA4pjHit

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