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    Question

    Find the least 4-digit number which, when divided by 9,

    12, and 15, leaves a remainder of 4 in each case.
    A 1,084 Correct Answer Incorrect Answer
    B 1,164 Correct Answer Incorrect Answer
    C 1,244 Correct Answer Incorrect Answer
    D 1,324 Correct Answer Incorrect Answer

    Solution

    Prime factorization of 9 = 3┬▓
    Prime factorization of 12 = 2┬▓ ├Ч 3
    Prime factorization of 15 = 3 ├Ч 5 LCM of (9, 12, and 15) = 2┬▓ ├Ч 3┬▓ ├Ч 5 = 180 Least 4-digit number divisible by 180 = 1,080 So, required number = 1080 + 4 = 1,084 Hence, option A.

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