An Instructor pilot reported taking evasive action in order to avoid traffic reported by SCT after departing LGB and climbing out VFR on a training flight.

Narrative

I was acting PIC; as an instructor in the right seat. Long Beach airport ATIS information reported visibility 5 SM; and sky 2;100 scattered. We departed Long Beach airport VFR heading southwest. Approximately 5 NM from LGB; I observed that the sky was broken with estimated ceiling of 2;100 MSL. We remained in level flight; VFR at 1;500 MSL. I contacted SCT Approach and requested an IFR clearance for IFR to VFR on top. The tops were estimated to be 2;500 MSL. SCT Approach issued an alert for traffic at 11 or 12 o'clock. I reported that I was looking for traffic. At this time the sky condition became clear above and ahead of us. I initiated a climb and remained VFR throughout the climb. At that time we saw the traffic at our 11 o'clock and approximately 1/4 mile and slightly below our altitude. I continued the climb to remain clear the other traffic's flight path. We passed over the traffic by approximately 300 FT. As we were able to remain VFR throughout the climb; I informed SCT Approach that we would not require IFR to VFR on Top; but asked for VFR traffic advisories.