Let x be the least number which when divided by 30, 36, 40 and 54, leaves a remainder of 4 in each case, and x is divisible by 23. What is…

Explanation

LCM of 30, 36, 40 and 54 is 1080, so x = 1080k + 4. Since 1080 leaves remainder 22 on division by 23, 22k + 4 must be divisible by 23, giving k = 4 and x = 4324. The digit sum is 13.