HCF and LCM of two numbers are 8 and 320 respectively. If one of the numbers is 64, find the other number?

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

The solution relies on the fundamental theorem of arithmetic concerning HCF and LCM, which states that for any two positive integers, their product is equal to the product of their HCF and LCM.
Let the two numbers be A and B. The formula is: A × B = HCF(A, B) × LCM(A, B).
Given values are: HCF = 8, LCM = 320, and one number (A) = 64.
Substituting the values into the formula gives: 64 × B = 8 × 320.
Calculating the product on the right side: 8 × 320 = 2560.
To find the other number (B), we divide this product by the known number: B = 2560 / 64, which equals 40.

Option B: This is double the correct answer and results from a calculation error, perhaps by incorrectly simplifying the fraction (e.g., 320 / (64/8) = 320/8 = 40, but a mistake could lead to 80).
Option C: This value is half of the given number (64) and might be chosen by guessing or a conceptual error, not by applying the correct formula.
Option D: This is another multiple of 8 but does not satisfy the HCF × LCM product rule. It is likely a result of miscalculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relationship between HCF, LCM, and the product of two numbers as background academic context rather than a clinical decision trigger.
While not a direct clinical scenario, this question tests basic arithmetic and logical reasoning. These skills are essential for nurses in tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data.
Proficiency in mathematics ensures patient safety by preventing calculation errors that could lead to incorrect dosages or infusion rates.
What if? If the LCM was 640 and the HCF was 4, the other number would be (640 × 4) / 64 = 2560 / 64 = 40. The answer remains the same, demonstrating how different HCF/LCM pairs can yield the same result for a given number.

How to Approach the Question

First, identify all the given values from the question: HCF = 8, LCM = 320, and one of the numbers is 64.
Recall the fundamental formula that connects these values for any two numbers: Product of the numbers = Product of their HCF and LCM.
Set up the equation based on the formula. Let the unknown number be 'x'. The equation becomes: 64 × x = 8 × 320.
Solve for 'x'. Start by calculating the product on the right side of the equation: 8 × 320 = 2560.
Isolate 'x' by dividing the product by the known number: x = 2560 / 64.
Perform the division to find the value of x, which is 40. Finally, match this result with the given options.

Concept Tested & Keywords

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