A 3 digit number is divided by 3,4,6,15, and 20, The remainder in each case is 1 the sum of the digit of the number

LCM IF 3,4,6,15 AND 20 IS 60
THE REQUIRED 3 DIGIT NUMBER IS 2*60+1= 121
AND THE SUM OF IT'S DIGIT= 1+2+1=4
HENCE THE ANWER IS 4

L.C.M of 3,4,6,15 and 20 is 60.
Now check the greatest 3-digit numbers which are divisible by 60.
The numbers are : 900 and 960
Add 1 to these numbers then - 901 and 961 (check it by using divisibility rules)
From these 961 is the answer (Greatest)

Now check the smallest 3-digit number which is divisible by 60.
The number is 120. Add 1 to this number-121
From this, 121 is the answer.

Hence,
The greatest 3- digit number is 961- Sum is : 16
The smallest 3-digit number is 121 - Sum is :4