En En 把所有 732 块饼干装进了一些大盒子和小盒子中。他每个大盒子装 30 块饼干，每个小盒子装 22 块饼干。所有的盒子都装满了，且没有剩下任何饼干。 En En 最少使用了多少个盒子？ 答: ___

1. Set up the equation for the total number of cookies.

Let the number of large boxes be $x$ and the number of small boxes be $y$.
$30x + 22y = 732$
Dividing by 2 to simplify:
$15x + 11y = 366$

2. Find the maximum possible number of large boxes to minimize the total number of boxes.

To use the least number of boxes, we must use as many large boxes as possible.
The maximum possible value for $x$ is $366 \div 15 = 24.4$, so we test integer values of $x$ starting from $24$ downwards to see which gives a whole number for $y$.
If $x = 24$, $11y = 366 - 15(24) = 6$ (not divisible by 11)
If $x = 23$, $11y = 366 - 15(23) = 21$ (not divisible by 11)
If $x = 22$, $11y = 366 - 15(22) = 36$ (not divisible by 11)
If $x = 21$, $11y = 366 - 15(21) = 51$ (not divisible by 11)
If $x = 20$, $11y = 366 - 15(20) = 66$, so $y = 6$.

3. Calculate the least total number of boxes.

Total number of boxes = $x + y = 20 + 6 = 26$.