What is the smallest number greater than 16 which, when divided by 6, 10 and 16, 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 6, 10 and 16) + 4. The smallest common multiple is the LCM: LCM(6, 10) = 30 and LCM(30, 16) = 240. So the number is 240 + 4 = 244. (4 itself also leaves remainder 4, but it is not greater than 16.) Check: 244 ÷ 6 leaves 4, ÷ 10 leaves 4, and ÷ 16 leaves 4.