In a class, 60% and 68% of students passed their Physics and Mathematics examinations respectively. Then at least ___________percentage of students passed both their Physics and Mathematics examinations.

Let us assume that there are a total of 100 students. 60% of the students passed in physics, thus 60 students passed physics. 68% students passed in math, thus 68 students passed in math.

Let us assume that x students passed in both the Math and Physics exams, and let n students didn't pass in both exams. 

=> n + (60-x) + x + (68-x) = 100

=> n + 128 - x = 100

=> x = 28 + n

The least value of n can be 0, and therefore, the least value of x will be 28. 

Thus, at least 28% students passed in both the Math and Physics exams.