Question
Find the least 4-digit number which is when divided by
16, 20, and 24 leaves a remainder of 9 in each case.Solution
Prime factorization of 16 = 2⁴ Prime factorization of 20 = 2² × 5 Prime factorization of 24 = 2³ × 3 LCM of (16, 20, 24) = 2⁴ × 3 × 5 = 240 Least 4-digit number divisible by 240 = 1,200 So, required number = 1200 + 9 = 1,209
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