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    Question

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

    21, 28, and 12, leaves a remainder of 3 in each case.
    A 1,011 Correct Answer Incorrect Answer
    B 1,215 Correct Answer Incorrect Answer
    C 1,119 Correct Answer Incorrect Answer
    D 1,323 Correct Answer Incorrect Answer

    Solution

    Prime factorization of 21 = 3 ├Ч 7
    Prime factorization of 28 = 2┬▓ ├Ч 7
    Prime factorization of 12 = 2┬▓ ├Ч 3 LCM of (21, 28, and 12) = 2┬▓ ├Ч 3 ├Ч 7 = 84 Least 4-digit number divisible by 84 = 1,008 So, required number = 1008 + 3 = 1,011 Hence, option A.

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