The average of seven consecutive positive integers is 126. The smallest of these integers is : 

Given:

The average of seven consecutive positive integers is 126.

Formula used:

Average of n consecutive integers = Middle integer

For seven consecutive integers, the middle integer is the fourth integer.

Calculation:

Average = 126

⇒ Middle integer = 126

⇒ Fourth integer = 126

⇒ The integers are: (126 - 3), (126 - 2), (126 - 1), 126, (126 + 1), (126 + 2), (126 + 3)

⇒ The smallest integer = 126 - 3 = 123

∴ The correct answer is 123.