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    Question

    The Least Common Multiple (LCM) and Highest Common

    Factor (HCF) of two numbers add up to 765. The LCM is 50 times the HCF. Given that one of the numbers is 75, determine the other number.
    A 124 Correct Answer Incorrect Answer
    B 130 Correct Answer Incorrect Answer
    C 150 Correct Answer Incorrect Answer
    D 132 Correct Answer Incorrect Answer

    Solution

    ATQ, Let the HCF be x and LCM be 50x. According to the question, x+50x=765. Solve for x: 51x=765 ⇒ x=15. HCF = 15, LCM = 750. The product of two numbers = HCF × LCM = 15×750=11250. Given one number is 75, the other number = 11250 /75=150. The other number is 150.

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