Cube-shaped box

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

Result

a =  30 cm
b =  1000

Solution:

$3 = 3 \\ 5 = 5 \\ 6 = 2 \cdot 3 \\ LCM(3, 5, 6) = 2 \cdot 3 \cdot 5 = 30\\ \ \\ \ \\ a = LCM(3,5,6) = 30 = 30 \ \text{ cm }$
$b = (30/3)^{ 3 } = 1000$

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