• # question_answer What is the sum of the digits of the least number which when divided by 52, leaves 33 as remainder, when divided by 78 leaves 59 and when divided by 117, leaves 98 as remainder?                                            A)  17                              B)  18                    C)                                 19                              D)  21

Here, $52-33=78-59=117-98=19$ Now, $52=13\times 2\times 2$ $78=13\times 2\times 3$ $117=13\times 3\times 3$ $\therefore$ LCM $=13\times 2\times 2\times 3\times 3=468$ $\therefore$ Required number $=468-19=449$ Hence, the sum of digits is 17.