Determine the number of ordered pairs of positive integers (a , b) such that the atleast common multiple of a and b is `2^(3)5^(7)11^(13)` .

Explanation

To determine the number of ordered pairs of positive integers (a, b) such that the least common multiple (LCM) of a and b is \(2^3 \cdot 5^7 \cdot 11^{13}\), we can follow these steps:

### Step 1: Express a and b in terms of their prime factors
Let:
- \(a = 2^{x_1} \cdot 5^{y_1} \cdot 11^{z_1}\)
- \(b = 2^{x_2} \cdot 5^{y_2} \cdot 11^{z_2}\)

### Step 2: Set up the conditions for the LCM
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