Question

    The LCM of the two numbers is 12 times their HCF. The

    sum of LCM and HCF is 429 and if both the number are smaller than their LCM. Find both numbers.
    A 64, 96 Correct Answer Incorrect Answer
    B 32,142 Correct Answer Incorrect Answer
    C 93,124 Correct Answer Incorrect Answer
    D 99,132 Correct Answer Incorrect Answer

    Solution

    LCM =12 HCF LCM: HCF = 12:1 ATQ-       13 = 429 1 = 33 HCF = 33 LCM = 33×12 = 396 Let the no 33x and 33y. As we know the product of two numbers = product of HCF & product of LCM 33x ×33y = 33 ×33×12 x y = 12 We cannot take values of x & y = 2 & 6 because these have 2 in common extra but there must be nothing common as 12 HCF is already taken. If values of x, y is (1, 12) ⇒ 1 × 33 = 33, 33 × 12 = 396 → not less than LCM If values of x, y is (3, 4) ⇒ 3 × 33, 4 × 33 = 99, 132.

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