Question

A rectangular block 6cm by 12cm by 15cm is cut up into an exact number of equal cubes.Find the least possible number of cubes

Answer 1

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$volume \: of \: cuboid = l \times b \times h \\ \\ now... \\ \\ let \: the \: no. \: of \: cubes \: be \: n \: then \\ \\ smallest \: dimensions \: of \: cube \: = 1 \times 1 \times 1 \\ \\ ..............solution............. \\ n \times {a}^{3} = 6 \times 12 \times 15 \\ \\ n \times 1 = 6 \times 12 \times 15 \\ \\ n = 72 \times 15 \\ \\ n = 1080 \\ \\ hence \: total \: no. \: of \:cubes \: = 1080 \: pieces \:$