108=2×2×3×3×3;

144=2×2×2×2×3×3;

72=2×2×2×3×3;

The greatest common divisor of 108, 144 and 72 is: 2× 2× 3× 3 = 36;

So this big class has at most 36 children.

A: There are at most 36 children in this large class.

So the answer is: 36.