how many ls gates can a standard ttl gate drive?

Standard ttl gate fanout is about 10 (this can vary and should be checked against the datasheet).

Fan-in for LS gates is about one tenth of TTL, so one TTL gate can drive about 100 LS gates. Note. This is an approximation (rule of thumb) and there are formula for calculating. Inputs of real gates have capacitance as well as resistance to the power supply rails. This capacitance will slow the output transition of the previous gate and hence increase its propagation delay. As a result rather than a fixed fanout the designer is faced with a trade off between fanout and propagation delay (which affects the maximum speed of the overall system).