The ratio of three numbers is 4 : 3 : 13. If their LCM is 4524, find the HCF…

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The ratio of three numbers is 4 : 3 : 13. If their LCM is 4524, find the HCF of the numbers.

  1. A.

    21

  2. B.

    29

  3. C.

    45

  4. D.

    49

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Correct answer: B

Let the three numbers be 4x, 3x, and 13x. Since 4, 3, and 13 are pairwise co-prime, the HCF of the three numbers is x.

  1. LCM relation: LCM(4x, 3x, 13x) = 4 x 3 x 13 x x = 156x

  2. Given: 156x = 4524

  3. Solve: x = 4524 / 156 = 29

Therefore, the HCF is 29.

Answer: 29

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