How many ways can you make a rectangular prism using 27 blocks?

To form a rectangular prism using 27 blocks, you need to find sets of integer dimensions ( (l, w, h) ) such that ( l \times w \times h = 27 ). The factorization of 27 is ( 3^3 ), leading to the following combinations for ( (l, w, h) ): ( (1, 1, 27), (1, 3, 9), (3, 3, 3) ), and their permutations. Since the order of dimensions matters, you need to count distinct permutations for each combination, resulting in a total of 10 unique arrangements.