Final answer:
The smallest number of chocolates in a box that leaves 4 remaining when shared among 8, 10, or 12 children is 124 chocolates, found by adding the least common multiple of the numbers (120) with the remainder (4).
Step-by-step explanation:
How to Find the Smallest Number of Chocolates in a Box
The question asks for the smallest number of chocolates in a box that when distributed among 8, 10, or 12 children, always leaves 4 chocolate bars remaining. This type of problem involves finding the least common multiple (LCM) of the given numbers and then accounting for the remainder.
Understand
We need to find the smallest box size that has 4 extra chocolates when shared among 8, 10, or 12 children.
Given
When the chocolates are divided among 8, 10, or 12 children, 4 are always left over.
Plan
To solve this problem, we'll find the LCM of 8, 10, and 12, and then add the remainder to it.
Solve
The LCM of 8, 10, and 12 is 120. Since there are always 4 chocolate bars left, the smallest number of chocolates in the box would be LCM + remainder, which is 120 + 4 = 124 chocolates.
Answer
The smallest number of chocolates in the box is 124 chocolates.