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Hi,
If I am understanding you well, you are referring to the periodic VS perpetual systems, right? If that’s the case, then LIFO and FIFO are not “under” one of these two. They are inventory valuation methods, and these methods can be used under either a periodic system or a perpetual one.
Periodic vs perpetual systems refer to how companies value their COGS and inventory, either at the end of the accounting period ( as in periodic) or continuously (as in perpetual).
Hope that helps !