Question
Find the least 4-digit number which is when divided by
18, 30, and 45 leaves a remainder of 7 in each case.Solution
Prime factorization of 18 = 2 × 3² Prime factorization of 30 = 2 × 3 × 5 Prime factorization of 45 = 3² × 5 LCM of (18, 30, 45) = 2 × 3² × 5 = 90 Least 4-digit number divisible by 90 = 1,080 So, required number = 1080 + 7 = 1,087
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