Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($) $ in Millions	9 Months Ended
	May 31, 2022	May 31, 2021
Goodwill [Roll Forward]
Goodwill, Beginning Balance	$ 1,094.7	$ 1,080.0
Adjustments to provisional amounts from acquired businesses	0.6
Additions from acquired businesses		3.1
Foreign currency translation adjustments	(4.4)	13.1
Goodwill, Ending Balance	1,090.9	1,096.2
ABL
Goodwill [Roll Forward]
Goodwill, Beginning Balance	1,022.2	1,012.6
Adjustments to provisional amounts from acquired businesses	0.6
Additions from acquired businesses		0.0
Foreign currency translation adjustments	(4.3)	8.4
Goodwill, Ending Balance	1,018.5	1,021.0
ISG
Goodwill [Roll Forward]
Goodwill, Beginning Balance	72.5	67.4
Adjustments to provisional amounts from acquired businesses	0.0
Additions from acquired businesses		3.1
Foreign currency translation adjustments	(0.1)	4.7
Goodwill, Ending Balance	$ 72.4	$ 75.2