Question
Find the least 4-digit number which is when divided by
14, 18, and 35 leaves a remainder of 13 in each case.Solution
Prime factorization of 14 = 2 × 7 Prime factorization of 18 = 2 × 3² Prime factorization of 35 = 5 × 7 LCM of (14, 18, 35) = 2 × 3² × 5 × 7 = 630 Least 4-digit number divisible by 630 = 1,260 So, required number = 1260 + 13 = 1,273
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