What is the smallest number greater than 15 which, when divided by 9, 10 and 15, leaves a remainder of 4 in each case?

💡 Solution & Explanation

A number that leaves the same remainder 4 with each divisor is (a common multiple of 9, 10 and 15) + 4. The smallest common multiple is the LCM: LCM(9, 10) = 90 and LCM(90, 15) = 90. So the number is 90 + 4 = 94. (4 itself also leaves remainder 4, but it is not greater than 15.) Check: 94 ÷ 9 leaves 4, ÷ 10 leaves 4, and ÷ 15 leaves 4.