Two cells ring at intervals of 78 seconds and 46 seconds. If they both ring at 10 O'clock in the morning together, after how many seconds will they ring together again?

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-2)

Explanation

The problem asks for the next time two events, occurring at different regular intervals, will happen simultaneously. This is a classic application of the Least Common Multiple (LCM).
The intervals are 78 seconds and 46 seconds.
First, find the prime factors of each number: 78 = 2 × 3 × 13 and 46 = 2 × 23.
The LCM is the product of the highest powers of all unique prime factors from both numbers.
LCM = 2 × 3 × 13 × 23 = 1794.
Thus, the cells will ring together again after 1794 seconds.

Option B: This value is not a multiple of 78 (1804 ÷ 78 ≈ 23.12). For the cells to ring together, the time elapsed must be a multiple of both intervals.
Option C: This value is not a multiple of 78 (1784 ÷ 78 ≈ 22.87). It is a multiple of 46 (1784 / 46 = 38.78), but not both.
Option D: This value is not a multiple of either 78 (1774 ÷ 78 ≈ 22.74) or 46 (1774 ÷ 46 ≈ 38.56).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Least Common Multiple (LCM) as background academic context rather than a clinical decision trigger.
While this is a math question, the underlying concept of LCM is relevant in healthcare for scheduling and synchronization.
For example, it can be used to determine when multiple medications with different dosing schedules (e.g., one every 4 hours, another every 6 hours) will need to be administered at the same time. The LCM of 4 and 6 is 12, so both drugs would be given together every 12 hours.
What if? If the intervals were 60 seconds and 90 seconds, the LCM would be 180 seconds (3 minutes). The approach remains the same: find the LCM of the two intervals.

How to Approach the Question

First, read the question carefully to identify what is being asked. The keywords 'ring together again' for events with different 'intervals' point towards a synchronization problem.
Recognize that finding the next time two events will occur simultaneously requires calculating the Least Common Multiple (LCM) of their intervals.
List the two numbers from the problem: 78 and 46.
Calculate the LCM of these two numbers by using the prime factorization method.
Find the prime factors of 78 (2 × 3 × 13) and 46 (2 × 23).
Multiply the highest power of each unique prime factor (2 × 3 × 13 × 23) to get the LCM, which is 1794.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent-20 July 2019 (Shift-2)

Attempt every question from this paper in a timed mock, then review the full solution for each one.