Two bells ring at intervals of 88 seconds and 58 seconds. If they both ring at 10 O'clock in the morning together, after how many seconds will they ring together again?

1. A

   2662

2. B

   2552

3. C

   2772

4. D

   2442

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-1)

Explanation

• The time for two periodic events to occur simultaneously is found by calculating the Least Common Multiple (LCM) of their individual periods.
• The prime factorization of 88 is 2³ × 11, and for 58 is 2 × 29.
• The LCM is the product of the highest powers of all prime factors involved: 2³ × 11 × 29.
• Calculating this gives 8 × 11 × 29 = 2552 seconds.

Why Other Options Were Wrong

• Option A: This value does not correspond to the LCM of 88 and 58. It might be a result of a calculation error, such as miscalculating the product of the prime factors.
• Option C: This value is not the LCM of 88 and 58. It could be a result of a calculation error or finding the LCM of a different pair of numbers.
• Option D: This value is not the LCM of 88 and 58. It could be a simple miscalculation during the multiplication step (e.g., 88 x 27 or a similar error).

Related Visual

• Visual 1: Infographic - A flowchart showing the steps to find the LCM of two numbers: 1. Prime Factorize, 2. Identify highest powers of all primes, 3. Multiply them together.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the Least Common Multiple (LCM) for periodic events as background academic context rather than a clinical decision trigger.
• While this is a math question, the concept of LCM is used in healthcare for scheduling, such as planning medication administration cycles or coordinating treatments that occur at different frequencies to find when they will coincide.
• What if? If the bells rang at 8 seconds and 12 seconds, the LCM would be 24 seconds (LCM of 8=2³ and 12=2²x3 is 2³x3=24), a much shorter interval.

How to Approach the Question

• Step 1: Identify the core task. The question asks when two events with different periodic intervals will happen together. This is a classic signal for using the Least Common Multiple (LCM).
• Step 2: List the two intervals given: 88 seconds and 58 seconds.
• Step 3: Find the prime factors of each number. For 88, it's 2 x 2 x 2 x 11. For 58, it's 2 x 29.
• Step 4: To calculate the LCM, take the highest power of each unique prime factor from the lists. This gives 2³ (from 88), 11 (from 88), and 29 (from 58).
• Step 5: Multiply these factors together: 8 x 11 x 29 = 2552.
• Step 6: Match the result (2552) with the given options.

Concept Tested & Keywords

• Concept Tested: Calculating the Least Common Multiple (LCM) for periodic events.
• Stem keywords: bells, intervals, 88 seconds, 58 seconds, ring together
• Lead-in keywords: after how many seconds

Question ID

Q6cew2Sw41edKw3hkqLLiV

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