Prime factorising 392, we get, 392=2×2×2×7×7 =2 3 ×7 2 . We know, a perfect cube has multiples of 3 as powers of prime factors. Here, number of 2's is 3 and number of 7's is 2. Therefore, 392 is clearly not a perfect cube.
Here, we need to multiply another 7 to the factorization to make 392 a perfect cube. Hence, the smallest number by which 392 must be multiplied to obtain a perfect cube is 7.
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