President Carter is facing big political problems in California, and they are not just Sen. Edward M. Kennedy and Ronald Reagan. Independent John B. Anderson is threatening to take away Carter's liberal vote in November.

In the June 3 Democratic primary, The Los Angeles Times Poll found, Carter is holding a precarious five percentage-point lead over Kennedy in their battle for California's 306 national convention delegates, 18.4 percent of the total needed to nominate a candidate for the presidency.

Assuming he ultimately wins renomination, as expected, Carter must meet an even tougher California challenge in the fall, contesting Reagan -- the probable Republican nominee -- for the state's 45 electoral votes, 16.7 percent of the total needed to elect a president.

In a two man Carter-Reagan race, the poll found, the president trails the former California governor by just four percentage points.

But when Anderson is added to the mythical ballot, Carter's support plummets and the president finds himself struggling to finish higher than third.

Although Anderson no longer is running actively in the Republican primaries -- he is concentrating instead on trying to qualify his new independent candidacy for several state ballots in November -- he still is listed on the GOP primary ballot in California. i

The poll found Anderson getting 10 percent to George Bush's 9 percent, far behind Reagan's 76 percent.

The Times conducted telephone interviews with 1,094 registered California voters from May 4 through 8. The margin of error in this poll is 4 percent.