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    Question

    The LCM of two natural numbers is 15 times their HCF.

    If the product of given two numbers is 2160, then find the LCM of the numbers. 
    A 180 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 360 Correct Answer Incorrect Answer
    D 60 Correct Answer Incorrect Answer

    Solution

    Let the HCF of the number be 'H'.  So, LCM = 15H  Product of two numbers = Product of their HCF and LCM  So, 15H × H = 2160  Or, H² = 144  Or, H = 12 or H = –12  Since, HCF cannot be negative. So, H = 12  Therefore, LCM = 15 × 12 = 180

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