Three standard dice, one with 4 sides, one with 6 sides, and one with 10 sides are rolled. The probability that all three dice show the same number can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are positive coprime integers. What is the value of \(a + b?\)

**Details and assumptions**

A standard \(i\)-sided die has sides numbered \(1, 2, \ldots, i\) and each rolls with equal probability.

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