Identical cubes

From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm?

Correct answer:

n =  60

Step-by-step explanation:

a=12 dm b=16 dm c=20 dm  12=223 16=24 20=225 GCD(12,16,20)=22=4  x=GCD(a,b,c)=GCD(12,16,20)=4 dm  V1=a b c=12 16 20=3840 dm3 V2=x3=43=64 dm3  n=V1/V2=3840/64=60

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