Question
Find the least 4-digit number which is when divided by
12, 15, and 20 leaves a remainder of 7 in each case.Solution
Prime factorization of 12 = 2² × 3 Prime factorization of 15 = 3 × 5 Prime factorization of 20 = 2² × 5 LCM of (12, 15, 20) = 2² × 3 × 5 = 60 Least 4-digit number divisible by 60 = 1,020 So, required number = 1020 + 7 = 1,027
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