Today marks another "the first time in a long time" point for the Roys. After today, the Roys will officially lead the division by themselves the latest in the season since 1985. In 2003 the Roys lost the division lead on August 21st after losing 4-3 to the Twins. They would come back to tie on August 27th and 28th, but never led the division alone again that season.
In 1985 the the eventual world champions were still 1.5 games back on August 21st while holding a 65-52 record. The Royals didn't gain the lead in the division until September 6th, then lost it again before regaining it for good on October 3rd while holding on to beat out the Angels by 1 game.
In 1994 the Royals were 64-51 on August 10th when the strike finished the season, but were still 4 games out.
The only other notable team since 1985 was in 1989, and that team might have actually been better than the 85 world champs. On August 21st that team was 71-53, but still 4.5 games back. The closest they came to the division winning Oakland As was 1.5 games back on September 1st at 79-55. The Royals would peak at 25 games over .500 (85-60) on September 13th, but were still 3 games behind.