The ratio of the three numbers is 4:5:6. L.C.M of these numbers is 2460. What…

2023

The ratio of the three numbers is 4:5:6. L.C.M of these numbers is 2460. What is their H.C.F?

  1. A.

    41

  2. B.

    42

  3. C.

    67

  4. D.

    78

Show answer & explanation

Correct answer: A

For three numbers in the ratio a : b : c, write them as ax, bx, and cx, where x is their common factor. Then the LCM of the three numbers equals x × LCM(a, b, c), and their HCF equals x × HCF(a, b, c).

  1. Let the three numbers be 4x, 5x, and 6x (ratio 4:5:6).

  2. LCM(4, 5, 6) = 60, so the LCM of the three numbers is 60x.

  3. Given LCM = 2460, so 60x = 2460, giving x = 41.

  4. HCF(4, 5, 6) = 1 (4, 5, and 6 share no common factor greater than 1), so the HCF of the three numbers is 1 × 41 = 41.

Cross-check: the numbers are 4×41=164, 5×41=205, 6×41=246. Their LCM is 2²×3×5×41=2460 (matches), and their only common factor is 41, confirming the HCF is 41.

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