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Numbers given LCM, HCF and ratio

CMAT 2020 · Quantitative Techniques & Data Interpretation · Easy · Number Systems

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The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of two numbers is 1 : 4, then the larger among two numbers is:

  1. A.

    28

  2. B.

    48

  3. C.

    88

  4. D.

    84

Answer

D

Explanation

Let the numbers be xx and 4x4x.

Product of numbers = LCM×HCF\text{LCM} \times \text{HCF} x×4x=84×21⇒4x2=1764⇒x2=441⇒x=21x \times 4x = 84 \times 21 \Rightarrow 4x^2 = 1764 \Rightarrow x^2 = 441 \Rightarrow x = 21.

Larger number = 4x=4×21=844x = 4 \times 21 = 84.

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