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Question Of The Day

    For positive integers a & b, how many ordered pairs (a, b) are there, such that lcm of a & b is 1000?

    a) 64

    b) 49

    c) 36

    d) 25

     

    Ans: b)49

     

    1000 = 2353. So a = 2A5R, b = 2B5S, and max(A, b) = 3, max(R, S) = 3 (A, b) can be (0, 3), (1, 3), (2, 3), (3, 3), (3, 2), (3, 1), (3, 0). Thus there are 7 ways of choosing A, b. similarly 7 ways of choosing (R2S2). Hence 7.7 = 49 ways.

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