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    Question

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

    14, 35, and 20, leaves a remainder of 9 in each case.
    A 1,029 Correct Answer Incorrect Answer
    B 1,129 Correct Answer Incorrect Answer
    C 1,229 Correct Answer Incorrect Answer
    D 1,329 Correct Answer Incorrect Answer

    Solution

    Prime factorization of 14 = 2 ├Ч 7
    Prime factorization of 35 = 5 ├Ч 7
    Prime factorization of 20 = 2┬▓ ├Ч 5 LCM of (14, 35, and 20) = 2┬▓ ├Ч 5 ├Ч 7 = 140 Least 4-digit number divisible by 140 = 1,120 So, required number = 1120 + 9 = 1,129 Hence, option B.

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