The largest four digit numbers divisible by 2, 3, 4, 5 and 6 will be?

Appeared in: BSF Staff Nurse - 2015

Explanation

To be divisible by 2, 3, 4, 5, and 6, a number must be divisible by their Least Common Multiple (LCM).
The LCM of 2, 3, 4 (2²), 5, and 6 (2×3) is 2² × 3 × 5 = 60.
The problem is now to find the largest 4-digit multiple of 60.
The largest 4-digit number is 9999.
Dividing 9999 by 60 gives a quotient of 166 and a remainder of 39 (9999 = 166 × 60 + 39).
Subtracting the remainder from 9999 gives the largest multiple of 60: 9999 - 39 = 9960.

Option A: 1080 is divisible by 60 (1080 = 18 × 60), but it is not the largest four-digit number with this property.
Option B: 1260 is divisible by 60 (1260 = 21 × 60), but it is not the largest four-digit number with this property.
Option D: 9880 is not divisible by 60. When 9880 is divided by 60, it leaves a remainder of 40.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Finding the largest n-digit number divisible by a set of numbers using the Least Common Multiple (LCM) as background academic context rather than a clinical decision trigger.
This question tests basic numeracy and logical reasoning, which are foundational skills for nurses.
Nurses frequently perform calculations for medication dosages, IV drip rates, and fluid balance, all of which require accuracy and an understanding of mathematical principles.
A strong grasp of arithmetic ensures patient safety by preventing medication errors and ensuring correct treatment administration.

How to Approach the Question

First, understand the question: you need to find the LARGEST 4-digit number that can be divided by 2, 3, 4, 5, and 6 without a remainder.
Recognize that for a number to be divisible by a set of numbers, it must be a multiple of their Least Common Multiple (LCM).
Calculate the LCM of 2, 3, 4, 5, and 6. The LCM is 60.
Identify the largest possible number in the specified range, which is the largest 4-digit number: 9999.
Divide the largest number (9999) by the LCM (60) and find the remainder.
Subtract the remainder from the largest number (9999) to get the final answer. This result will be the largest multiple of the LCM within that range.

Concept Tested & Keywords

Concept Tested: Finding the largest n-digit number divisible by a set of numbers using the Least Common Multiple (LCM).
Stem keywords: largest, four digit, divisible by, 2, 3, 4, 5 and 6
Lead-in keywords: BEST, MOST RELEVANT CLUE

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Practise the full BSF Staff Nurse - 2015

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