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Earnings Per Share (Basic and Diluted Earnings per Share - Treasury Stock Method) (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended						9 Months Ended
	May 31, 2019	Feb. 28, 2019	Nov. 30, 2018	May 31, 2018	Feb. 28, 2018	Nov. 30, 2017	May 31, 2019	May 31, 2018
Earnings Per Share [Abstract]
Net Income	$ 88.4	$ 66.3	$ 79.6	$ 73.0	$ 96.9	$ 71.5	$ 234.3	$ 241.4
Basic weighted average shares outstanding (in shares)	39.7			40.4			39.8	41.2
Common stock equivalents (in shares)	0.1			0.1			0.1	0.1
Diluted weighted average shares outstanding (in shares)	39.8			40.5			39.9	41.3
Basic earnings per share (in dollars per share)	$ 2.23			$ 1.81			$ 5.89	$ 5.86
Diluted earnings per share (in dollars per share)	$ 2.22			$ 1.80			$ 5.87	$ 5.85

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