彼得有许多长宽高分别为 24 厘米、20 厘米和 15 厘米的长方体木块。他希望制造一个正方体形状的箱子来装这些木块，使得箱内没有空隙。
求箱子最小可能的边长。 答 ... 厘米

1. Recognise that the cube side length must be a common multiple of all three block dimensions.

For the cuboid blocks to fit with no empty space in a cube, the side length of the cube must be divisible by $24$, $20$ and $15$.

So the smallest possible side length is
$\operatorname{LCM}(24,20,15).$

2. Find the LCM of the three dimensions.

Prime factorise:
$24=2^3\times 3,$
$20=2^2\times 5,$
$15=3\times 5.$

Taking the highest powers of each prime,
$\operatorname{LCM}=2^3\times 3\times 5=120.$