1. The problem is to simplify the expression $\frac{10\pi}{6}$.\n\n2. The formula used here is to simplify fractions by dividing numerator and denominator by their greatest common divisor (GCD).\n\n3. Find the GCD of 10 and 6, which is 2.\n\n4. Divide numerator and denominator by 2:\n$$\frac{\cancel{10}^5\pi}{\cancel{6}^3} = \frac{5\pi}{3}$$\n\n5. The simplified form of $\frac{10\pi}{6}$ is $\frac{5\pi}{3}$.