LCM and HCF of two numbers is 84 and 21 respectively and the ratio of these…

2023

LCM and HCF of two numbers is 84 and 21 respectively and the ratio of these two numbers is 1:4. Find the greatest no.

  1. A.

    42

  2. B.

    84

  3. C.

    21

  4. D.

    25

Attempted by 21 students.

Show answer & explanation

Correct answer: B

Solution:

  1. Let the two numbers be k and 4k (since their ratio is 1:4).

  2. The highest common factor of k and 4k is k, so k must equal the given HCF 21.

  3. Thus the numbers are 21 and 84, and the greatest number is 84.

  4. Check: LCM = (21 × 84) / gcd(21,84) = (21 × 84) / 21 = 84, which matches the given LCM.

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