Find out the least number which should be added to 25 to generate a sum which…

To find the least number that must be added to a given number so it becomes exactly divisible by two or more divisors, first find the LCM of those divisors -- since any common multiple of the divisors is also a multiple of their LCM, the sum must equal the next multiple of the LCM at or above the given number. The amount to add equals (LCM minus remainder), where the remainder is what the given number leaves when divided by the LCM (the amount is 0 only when that remainder is already 0).

1. Find the LCM of 3 and 9. Since 9 is itself a multiple of 3, the LCM of 3 and 9 is 9.

2. Divide 25 by 9: 25 = 9 x 2 + 7, so the remainder is 7.

3. Since the remainder (7) is not 0, the number to add is LCM minus remainder = 9 minus 7 = 2.

4. Add 2 to 25 to get 27.

Check: 27 divided by 9 = 3 exactly and 27 divided by 3 = 9 exactly, confirming that 27 is divisible by both 3 and 9 -- so 2 is indeed the least number that must be added.