Cube-shaped box

Find the size of the smallest possible cube-shaped box where three types of 3cm, 5cm, and 6cm small cubes could be stacked to fully use the box space (each type of cube separately). Can you find out how many smallest cubes are in the box?

Correct answer:

a =  30 cm
b =  1000

Step-by-step explanation:

$$\begin{gathered} 3...\text{ prime number} \\ 5...\text{ prime number} \\ 6=2\cdot 3 \\ LCM(3,5,6)=2\cdot 3\cdot 5=30 \\ a=LCM(3,5,6)=30\text{cm} \end{gathered}$$

$b=(30/3{)}^3=1000$

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