What is the smallest number greater than 18 which, when divided by 8, 16 and 18, leaves a remainder of 1 in each case?

💡 Solution & Explanation

A number that leaves the same remainder 1 with each divisor is (a common multiple of 8, 16 and 18) + 1. The smallest common multiple is the LCM: LCM(8, 16) = 16 and LCM(16, 18) = 144. So the number is 144 + 1 = 145. (1 itself also leaves remainder 1, but it is not greater than 18.) Check: 145 ÷ 8 leaves 1, ÷ 16 leaves 1, and ÷ 18 leaves 1.