The Sunday marches, called by rights activists, also served as an opportunity for people to protest against Trump's immigration policies, his business ties abroad and possible Russian interference in the 2016 presidential election, Efe news reported.
Suspicions that Trump obstructed justice and has violated the foreign emoluments clause would both be constitutionally valid reasons for Congress to investigate and impeach the President, said Tudor Popescu of the Indivisible CA D-39 group, the main organiser of the march here.
The Los Angeles demonstration was the largest of those called around the US with about 10,000 participants, according to organisers.
Protesters held signs that read "Worst President Ever" and chanted "Down, down, down with Trump - up, up, up with the people" as they urged US Congress to impeach the President, showed images and video footage from the scene.
Organisers believe Trump has "been in blatant violation of the Constitution from the day he was sworn into the office of President".
Trump "has committed Constitutional breaches, consistently lied, cheated, and enforces laws that primarily benefit him and his billionaire friends at the expense of the country", said the organisers' website.
However, the great majority of the other 46 marches had only scanty turnout.
One of those was in New York where only a few dozen people showed up to protest in front of the Trump International Hotel, where they were joined by a group showing support for the President. No incidents or altercations developed.
In Palm Beach, Florida, marchers ended up in front of Trump's Mar-a-Lago exclusive club, where the President has spent a number of weekends since being inaugurated.
Among the dozens of other cities which held marches were Atlanta, Austin, Chicago and New Orleans.