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    Question

    The HCF of two numbers is 18 and their LCM is 540. If

    one of the numbers is 90, find the other number.
    A 274 Correct Answer Incorrect Answer
    B 108 Correct Answer Incorrect Answer
    C 113 Correct Answer Incorrect Answer
    D 197 Correct Answer Incorrect Answer

    Solution

    For two numbers a and b: a ├Ч b = HCF ├Ч LCM Let the other number be x. 90 ├Ч x = 18 ├Ч 540 Compute RHS: 18 ├Ч 540 = 18 ├Ч (54 ├Ч 10) = (18 ├Ч 54) ├Ч 10 18 ├Ч 54 = (20 тИТ 2) ├Ч 54 = 1,080 тИТ 108 = 972 So 972 ├Ч 10 = 9,720 So 90x = 9,720 x = 9,720 / 90 = 108 Answer: The other number = 108.

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