Question
Find the least 4-digit number which, when divided by 9,
12, and 15, leaves a remainder of 4 in each case.Solution
Prime factorization of 9 = 3²
Prime factorization of 12 = 2² × 3
Prime factorization of 15 = 3 × 5 LCM of (9, 12, and 15) = 2² × 3² × 5 = 180 Least 4-digit number divisible by 180 = 1,080 So, required number = 1080 + 4 = 1,084 Hence, option A.
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