Doing so is one of the five pillars of Islam, expected of all able-bodied believers at least once in their lives.
It begins with men donning a white sheath made from two pieces of material. They do this before entering the sacred city, so, for example, airports in places such as Istanbul, Turkey, which may be the last stop before Saudi Arabia, can be a sea of white.
Women wear robes of any color, but must cover their heads.
The rituals include throwing pebbles at pillars, which symbolize Satan, and celebrating in front of the Kaaba, or black stone, at the center of an open-air mosque. The stone represents the altar upon which Muslims believe the Prophet Abraham nearly sacrificed his son Ishmael (Christianity and Judaism teach that it was Isaac on the altar).
The crowd then circles the stone seven times, as a religious re-enactment of the frantic search by Abraham's wife, Hagar, for water for Ishmael in the barren valley. As the story goes, she ran between two hills seven times and a spring bubbled up under the child's feet.
This year's hajj throngs thinned by about a million from last year's because the Saudis gave out about 20 percent fewer visas, partly due to construction going on in Mecca and partly because of a health scare associated with MERS (Middle East Respiratory Syndrome).
Still, millions of worshippers packed a limited space, says Shuaib Din, imam of the Utah Islamic Center in Sandy who has acted as a hajj spiritual guide and teacher for four years. "People coming to hajj for the first time couldn't tell."
The logistics are a nightmare, he says. "It is not possible for humans to organize it. They could not pull it off without divine help."
Crowd control was one of Bymaster's concerns, too. She worried about being trampled or lost in the hordes.
In the end, she, too, was amazed by the peacefulness and patience she experienced.
It took, for example, nearly eight hours to get from the airport in Mecca to the main mosque, a distance of only a few miles. But pilgrims waited for buses without complaint or aggression, she says. And, during the rituals, no shoving occurred.
"When I got to touch the Kaaba, it was not an easy feat," Bymaster says. "But it was awesome. I choked up being in this holy place."
She was humbled, she says, by her sense of economic privilege.
"My experience was easy compared to some people who, in order to fulfill this pillar, sleep on the street with only one pair of clothes and the sheaths," Bymaster says. "The only thing I had to worry about was being in contact with people, or with the dust and smog. Shuaib and the travel agency took care of everything."
The Utah woman, like others who went with her, was struck by the diversity of believers.
"Standing in one corner, I saw 10 different shades of color in people's faces," she says. "You feel this sense of wow."
It was impressive to see so many people "united in purpose," says Daanish Hoda, an oncologist at LDS Hospital who was in Bymaster's group. "Watching hundreds of thousands of people walking in concert, saying the same thing, was a very moving experience."
You definitely "come back stronger," Hoda says, "and more connected."
For Faisal Ahmed, a Salt Lake City-born medical student who just finished his residency, hajj marked a spiritual renewal.
Ahmed had been living in New York, where he felt distracted by all the choices.
His trip to Saudi Arabia helped him refocus, he says. "To be frank, it brought me back to my faith."
Five pillars of Islam
• Acknowledge that there is no God but Allah and that Muhammad was his prophet.
• Pray five times a day, with prescribed prayers at prescribed hours.
• Observe the holy month of Ramadan.
• Give alms to the poor.
• Make a pilgrimage to Mecca during the hajj at least once in a lifetime.