The wooden

The wooden block measures 12 cm, 24 cm, and 30 cm. Peter wants to cut it into several identical cubes. At least how many cubes can he get?

Correct answer:

x =  40

Step-by-step explanation:

$$\begin{gathered} a=12\text{ cm } \\ b=24\text{ cm } \\ c=30\text{ cm } \\ 12=2^2\cdot 3 \\ 24=2^3\cdot 3 \\ 30=2\cdot 3\cdot 5 \\ \text{GCD}(12,24,30)=2\cdot 3=6 \\ d=GCD(a,b,c)=GCD(12,24,30)=6\text{ cm } \\ V=a\cdot b\cdot c=12\cdot 24\cdot 30=8640{\text{cm}}^3 \\ {V}_1=d^3=6^3=216{\text{cm}}^3 \\ x=V\mathrm{/}{V}_1=8640\mathrm{/}216=40 \end{gathered}$$

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