B737 Captain reports descent below published altitude during transition from SEAVU fix to the ILS 24R at LAX. Deviation occurred after the second runway change during the arrival.

Narrative

While flying the SEAVU 2 Arrival to LAX; we were planning the 24R approach. We planned; briefed; and loaded the approach into the FMC. Approach gave us the arrival to 25L. We made the necessary changes and briefed and loaded the new approach. Then they changed the arrival back to 24R. We reloaded that approach. During the transition from the arrival to the approach; we crossed SEAVU fix at 10;000 ft and continued to descend to 9500 ft. We should have maintained 10;000 ft until crossing the next fix which was SKOLL. The First Officer was using the autothrottle and VNAV functions but didn't notice the descent below 10;000 ft as the workload went up during the runway changes. I was the PM but didn't catch the descent until we were below 10;000 ft. Both Pilots need to improve their proficiency using VNAV and autothrottle. We both thought it was going to maintain the descent profile. Even though the workload went up; I should ensure the aircraft was doing what we thought it was going to do.