What is the smallest number greater than 20 which, when divided by 15, 16 and 20, leaves a remainder of 8 in each case?

💡 Solution & Explanation

A number that leaves the same remainder 8 with each divisor is (a common multiple of 15, 16 and 20) + 8. The smallest common multiple is the LCM: LCM(15, 16) = 240 and LCM(240, 20) = 240. So the number is 240 + 8 = 248. (8 itself also leaves remainder 8, but it is not greater than 20.) Check: 248 ÷ 15 leaves 8, ÷ 16 leaves 8, and ÷ 20 leaves 8.