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    Question

    Two numbers have LCM 360 and HCF 12. If one of the

    numbers is 72, find the other number. Also find how many common divisors the two numbers have.
    A 12 Correct Answer Incorrect Answer
    B 6 Correct Answer Incorrect Answer
    C 8 Correct Answer Incorrect Answer
    D 10 Correct Answer Incorrect Answer

    Solution

    For two numbers a and b: a × b = LCM × HCF Let other number be x. 72 × x = 360 × 12 72x = 4320 ⇒ x = 4320 / 72 = 60 Other number = 60. Common divisors of the two numbers are the divisors of their HCF = 12. Prime factorization of 12 = 2² × 3¹ Number of divisors = (2 + 1)(1 + 1) = 3 × 2 = 6 So they have 6 common divisors.

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