One pouch is enough, but one focus isn't
A character can use a component pouch or a spellcasting focus in place of the components specified for a spell. (Player's Handbook, page 203)
So far, no restriction on which focus a character can use on which spell. However, both classes state that their focus is valid for the specific class's spells only:
You can use a holy symbol (found in chapter 5) as a spellcasting focus for your cleric spells. (Player's Handbook, page 58)
You can use an arcane focus (found in chapter 5) as a spellcasting focus for your sorcerer spells. (Player's Handbook, page 101)
And even explicitly stated in the multiclassing rules:
...a spellcasting focus, such as a holy symbol, can be used only for the spells from the class associated with that focus. (Player's Handbook, page 164)
Note that association, here, refers to which class you learned the spell from, not the class spell lists. If you prepare a spell as a Cleric spell, you can't use an Arcane focus to cast it, even if the spell is on the Sorcerer spell list.
This makes the component pouch a better option for a multiclassed character going for flexibility, as it can always provide the simple (ones without a marked cost) material components for a spell regardless of its class.