What is the least number that should be added to 2480 so that the sum is exactly divisible by 3, 4, 5 and 6?

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

The core concept is that for a number to be divisible by a set of numbers, it must be divisible by their Least Common Multiple (LCM).
First, calculate the LCM of 3, 4, 5, and 6, which is 60.
Next, divide the given number, 2480, by the LCM (60). This gives a remainder of 20.
The number that needs to be added is the difference between the LCM and the remainder (60 - 20 = 40).
Adding 40 to 2480 gives 2520, which is the next multiple of 60 after 2480.

Option B: Adding 60 (the LCM itself) results in 2540. When 2540 is divided by 60, it leaves a remainder of 20, so it is not exactly divisible.
Option C: 20 is the remainder when 2480 is divided by the LCM (60). Adding the remainder (2480 + 20 = 2500) does not make the sum divisible by 60 (2500 ÷ 60 leaves a remainder of 40).
Option D: Adding 50 to 2480 gives 2530. When 2530 is divided by 60, it leaves a remainder of 10, so it is not exactly divisible.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Finding the least number to be added to a given number to make it exactly divisible by a set of other numbers as background academic context rather than a clinical decision trigger.
This is a general aptitude and reasoning question, not a clinical one.
This type of problem tests foundational mathematical skills, specifically number theory involving LCM and division, which are essential for logical reasoning and problem-solving in various fields.
What if the question asked for the least number to be subtracted? In that case, the answer would be the remainder itself, which is 20.

How to Approach the Question

Identify the core task: Find the smallest number to add to 2480 to make it divisible by 3, 4, 5, and 6.
Recognize that for a number to be divisible by several other numbers, it must be divisible by their Least Common Multiple (LCM).
Calculate the LCM of the divisors (3, 4, 5, 6).
Divide the given number (2480) by the calculated LCM and find the remainder.
The number to be added is the difference between the LCM and the remainder. This will bring the original number up to the next exact multiple of the LCM.
Verify your answer by adding the number to 2480 and checking if the sum is divisible by the LCM.

Concept Tested & Keywords

Concept Tested: Finding the least number to be added to a given number to make it exactly divisible by a set of other numbers.
Stem keywords: least number, added to 2480, exactly divisible, 3, 4, 5 and 6
Lead-in keywords: What is

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Practise the full DSSSB -28 August 2019 (Shift-2)

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