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Given, a number as 7803. We need to find out a number which if multiplied by the given number we get a perfect cube.

Step 1: Resolve 7803 into prime factors We get, 3 × 3 × 3 × 17 × 17

Step 2: Pair the factors obtained in the group of three

(3 × 3 × 3) × (17 × 17)

Step 3: multiply the number with the factor which is alone.

Here, 3 is in group of three and 17 is alone.

7803 × 17 = 132651

Hence, 17 is the smallest number which is to be multiplied to the given number for perfect cube.

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