The number of porper divisors of `2^(m)xx6^(n)xx15^(p)` , is

Options

A. `(m+n+1)(n+p+1)(p+1)`
B. `(m+n+1)(n+p+1)(p+1)-2`
C. `(m+n)(n+p)-2`
D. none of these

Explanation

To find the number of proper divisors of the expression \(2^m \times 6^n \times 15^p\), we can follow these steps:

### Step 1: Factor the expression
First, we need to express \(6\) and \(15\) in terms of their prime factors:
- \(6 = 2 \times 3\)
- \(15 = 3 \times 5\)

Thus, we can rewrite the original expression:
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