Quantitative Aptitude • Number System & SimplificationHard
What is the smallest number greater than 15 which, when divided by 9, 12 and 15, leaves a remainder of 7 in each case?
A. 173
B. 367
C. 180
D. 187✓ Correct Answer
💡 Solution & Explanation
A number that leaves the same remainder 7 with each divisor is (a common multiple of 9, 12 and 15) + 7. The smallest common multiple is the LCM: LCM(9, 12) = 36 and LCM(36, 15) = 180. So the number is 180 + 7 = 187. (7 itself also leaves remainder 7, but it is not greater than 15.) Check: 187 ÷ 9 leaves 7, ÷ 12 leaves 7, and ÷ 15 leaves 7.
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