No, it is not recommended to put a traditional cast iron skillet in the dishwasher. The high heat, strong detergents, and agitation in the dishwasher can strip away the seasoning, which is the protective layer on the surface of the cast iron pan. Additionally, the prolonged exposure to water can cause rusting. Instead, it's best to hand wash a cast iron skillet using hot water and a soft brush or sponge, avoiding soap.
As for enameled Dutch ovens, such as those made by Le Creuset, they are typically dishwasher safe. The enamel coating provides protection and prevents rusting. However, it's always a good idea to refer to the manufacturer's instructions for specific care and cleaning recommendations for your particular enameled Dutch oven. Some manufacturers may recommend hand washing to preserve the enamel's appearance and longevity.
In general, it's advisable to check the care instructions provided by the manufacturer for any cookware, as they can vary depending on the specific brand and materials used. Following the recommended cleaning methods will help ensure the longevity and performance of your cookware.