Passengers on the third flight said they didn't even know about the Singapore incident until their plane touched the ground.
It was the most serious midair incident involving the double-decker A380 since its debut in October 2007, and it was a terrifying experience for passengers.
"We heard a loud bang, and I was sitting right on the side where the engine is," said passenger Ulf Waschbusch.
The Qantas A380 flight had to make an emergency landing back where it departed in Singapore, six minutes after takeoff. Qantas CEO Alan Joyce described the incident as a "significant engine failure."
In Indonesia, what is believed to be debris from the plane was found at several locations, and on the plane itself, pieces were missing and burn marks were visible.
"We have decided that we will suspend all A380 takeoffs until we're fully comfortable that we have sufficient information ... about the QF32," Joyce said.
The aircraft landed safely at 11:45 a.m. local time, and it took two hours to get all 433 passengers on the flight evacuated safely. After the scare, passengers said they felt lucky to be alive.
The Airbus A380 is the largest plane in the world and can carry up to 535 passengers. Some people at LAX wondered if that was just too big.
"Is it meant to be that big? I don't know, I just want to get from point A to B safe," said Anna Garcia, who is a frequent flyer.
John Nance, ABC News aviation consultant, said he didn't see any indication that the incident had anything negative to say about the size of the Airbus A380s.
"This was just an engine, and I say 'just,' but that's actually a separate component of the airplane," he said.
The Airbus A380 has had no fatal accidents in the past, and Qantas has had no fatal accidents either.
L.A. passengers of canceled Qantas flights were put in hotel rooms to await departure on a different flight.
"We got on, we stayed on there for probably about 2-and-a-half hours, and after that they said, 'We're going to have to put you up in a hotel,'" said John Fallon, who was a passenger on one of the canceled flights.
But the Fallon family said they were willing to wait, as long as it meant they were safe.
The Associated Press contributed to this story.