The least common multiple of three different numbers is 800, which of the following cannot be their highest common factor?

Appeared in: CIP Ranchi 2023

Explanation

The fundamental rule connecting HCF and LCM is that the HCF of a set of numbers must be a factor of their LCM.
This means that the LCM must be perfectly divisible by the HCF, with no remainder.
The LCM is given as 800.
To solve the problem, we must find which of the given options is NOT a factor of 800.
Dividing 800 by 500 gives 1.6, which is not a whole number.
Therefore, 500 cannot be the HCF of any set of numbers whose LCM is 800.

Option A: This is incorrect because 200 is a factor of 800 (800 / 200 = 4). Therefore, it is possible for 200 to be the HCF.
Option B: This is incorrect because 100 is a factor of 800 (800 / 100 = 8). Therefore, it is possible for 100 to be the HCF.
Option D: This is incorrect because 400 is a factor of 800 (800 / 400 = 2). Therefore, it is possible for 400 to be the HCF.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relationship between Highest Common Factor (HCF) and Least Common Multiple (LCM) as background academic context rather than a clinical decision trigger.
This question tests general aptitude and mathematical reasoning, which is a component of many nursing entrance examinations.
While not a direct clinical skill, strong numeracy is crucial for nurses in daily practice for tasks such as calculating medication dosages, titrating IV drips, monitoring fluid balance charts, and interpreting lab values.
A nurse's ability to perform calculations accurately and quickly is a critical patient safety competency.

How to Approach the Question

First, identify the key information provided: The Least Common Multiple (LCM) is 800.
Next, understand the question's objective: You need to find which of the options cannot be the Highest Common Factor (HCF).
Recall the fundamental mathematical principle that connects HCF and LCM: The HCF of a group of numbers must always be a factor of their LCM.
Apply this rule by testing each option. Divide the LCM (800) by each of the potential HCFs given in the options.
If the division results in a whole number (no remainder), the option can be the HCF.
The option that results in a decimal or a fraction is the one that cannot be the HCF, and is therefore the correct answer.

Concept Tested & Keywords

Concept Tested: Relationship between Highest Common Factor (HCF) and Least Common Multiple (LCM)
Stem keywords: least common multiple, LCM, highest common factor, HCF, 800
Lead-in keywords: cannot be
Negative lead-in flag: Question asks what CANNOT be the HCF

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Practise the full CIP Ranchi 2023

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