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    Question

    The LCM of six consecutive numbers is 420. The

    sum of the first and fourth numbers is equal to the sixth number. What is the product of six numbers?
    A 3020 Correct Answer Incorrect Answer
    B 3120 Correct Answer Incorrect Answer
    C 5040 Correct Answer Incorrect Answer
    D 3320 Correct Answer Incorrect Answer

    Solution

    Therefore, 420 = 2 × 2 × × 3 × 5 × 7 i.e, numbers are 2, 3, 4, 5, 6 and 7 Therefore, products is = 2 × 3 × 4 × 5 × 6 × 7 = 5040 Alternate method: Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 Given that Sum of the first and fourth numbers is equal to the sixth number so, x + x + 3 = x + 5 x = 2 numbers are 2, 3, 4, 5, 6 and 7 Therefore, products is = 2 × 3 × 4 × 5 × 6 × 7 = 5040

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