Question
Find the least 4-digit number which, when divided by
14, 35, and 20, leaves a remainder of 9 in each case.Solution
Prime factorization of 14 = 2 × 7
Prime factorization of 35 = 5 × 7
Prime factorization of 20 = 2² × 5 LCM of (14, 35, and 20) = 2² × 5 × 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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