Step 1 :First, we convert the Fahrenheit temperature to Celsius using the formula \(C = \frac{5}{9}(F-32)\). Substituting \(F = 134\), we get \(C = \frac{5}{9}(134-32)\).
Step 2 :Calculating the above expression, we get \(C = \frac{5}{9}(102) = 56.67\).
Step 3 :Since we need to round to the nearest integer, the Celsius temperature is \(\boxed{57^\circ C}\).
Step 4 :Next, we convert the Celsius temperature to Kelvin using the formula \(K = C + 273.15\). Substituting \(C = 57\), we get \(K = 57 + 273.15\).
Step 5 :Calculating the above expression, we get \(K = 330.15\).
Step 6 :Since we need to round to the nearest integer, the Kelvin temperature is \(\boxed{330 K}\).