Find the smallest number which when multiplied with 137592 will make the product a perfect cube. Further, find the cube root of the product.

Explanation

To solve the problem of finding the smallest number which, when multiplied with 137592, results in a perfect cube, and to find the cube root of that product, we can follow these steps:

### Step 1: Prime Factorization of 137592
We need to start by factorizing the number 137592 into its prime factors.

1. **Divide by 2** (the smallest prime):
- 137592 ÷ 2 = 68796
- 68796 ÷ 2 = 34398
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