To find the least number that must be added to 308 to make it divisible by 19, we can follow these steps:

1. Divide 308 by 19 to determine the remainder:

   $308 \div 19 = 16 \text{ with a remainder of } 4.$

   This means that $308 = 19 \times 16 + 4$.

2. Subtract the remainder from 19 to find the difference that would make 308 divisible by 19:

   $19 - 4 = 15.$

3. Add 15 to 308 to make the number divisible by 19:

   $308 + 15 = 323.$

Thus, the least number that must be added to 308 to make it divisible by 19 is 15.

Would you like further clarification or additional details? Here are some related questions you might find interesting:

1. What is the remainder when 323 is divided by 19?
2. How can you find the least number that must be added to any number to make it divisible by a given divisor?
3. What is the division algorithm, and how does it relate to this problem?
4. How do you calculate the next multiple of 19 greater than 308?
5. Can you apply the same method to find the least number to add for divisibility by other numbers, like 7 or 13?

Tip: To check divisibility, always first find the remainder when dividing the number by the divisor, then subtract that remainder from the divisor to determine how much more is needed.