DJs routinely change the playback speed to match tempos.

It’s easier if a track’s tempo stays the same throughout its duration, but even if it changes, DJs will adjust the playback speed on the fly.

As far as syncing is concerned, the actual value of the tempos doesn't matter at all.

"Harder, Better, Faster, Stronger" was built around a one- or two-bar loop sampled from Edwin Birdsong's "Cola Bottle Baby."

Daft Punk determined that this loop had a tempo of 116.527 BPM and played it a semitone higher.

116,527 * 2 ^ (1 / 12) = 123,456 BPM