What is the smallest number greater than 24 which, when divided by 6, 20 and 24, 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 6, 20 and 24) + 1. The smallest common multiple is the LCM: LCM(6, 20) = 60 and LCM(60, 24) = 120. So the number is 120 + 1 = 121. (1 itself also leaves remainder 1, but it is not greater than 24.) Check: 121 ÷ 6 leaves 1, ÷ 20 leaves 1, and ÷ 24 leaves 1.