Set a steamer basket in a large pot. Fill with enough water to come just below basket; bring to a boil. Add potatoes; reduce to a simmer, cover, and cook until tender, 10 to 12 minutes. Transfer to a food processor.
Combine chickpeas, lemon juice, tahini, oil, cumin, and garlic in the food processor. Puree, about 1 minute; thin with water if necessary. Season with salt and pepper and let cool; refrigerate, in an airtight container, up to 1 week. Serve with pita and crudites.