For b-bit precision seeds, the period is
, or 
for multiplication,
for suitably chosen lags. This maximum period is only obtained when the
lags p and q satisfy certain mathematical properties. Lists of
suitable lags have been published.
Note that the period can be made arbitrarily large by increasing the largest lag (i.e. the size of the lag table). This is a very useful property for large-scale simulations. Empirical tests have shown that the randomness properties of these generators are also improved by increasing the lag.
Another very useful property of LFGs which use the operations + or - is that we can do all the computations modulo 1 on real numbers in the interval [0,1), and save having to do a multiplication to convert between integers and reals. These generators are consequently very fast.