The size 3

The size of a wooden block is 15cm × 12cm × 20cm. How many such blocks will be required to construct a solid wooden cube of minimum size?

Correct answer:

n =  60

Step-by-step explanation:

$$\begin{gathered} a=15\text{cm} \\ b=12\text{cm} \\ c=20\text{cm} \\ 15=3\cdot 5 \\ 12=2^2\cdot 3 \\ 20=2^2\cdot 5 \\ LCM(15,12,20)=2^2\cdot 3\cdot 5=60 \\ x=LCM(a,b,c)=LCM(15,12,20)=60\text{cm} \\ V=a\cdot b\cdot c \\ {n}_1=x/a=60/15=4 \\ {n}_2=x/b=60/12=5 \\ {n}_3=x/c=60/20=3 \\ n=n_1\cdot n_2\cdot n_3=4\cdot 5\cdot 3=60 \end{gathered}$$

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