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Comprehensive Income - Changes in Components of Accumulated Other Comprehensive Income (Loss) Items (Details) - USD ($) $ in Millions	3 Months Ended						9 Months Ended
	May 31, 2023	Feb. 28, 2023	Nov. 30, 2022	May 31, 2022	Feb. 28, 2022	Nov. 30, 2021	May 31, 2023	May 31, 2022
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	$ 1,947.6	$ 1,903.5	$ 1,911.8	$ 2,104.3	$ 2,072.9	$ 2,044.5	$ 1,911.8	$ 2,044.5
Other comprehensive income (loss) before reclassifications							2.6	(8.9)
Amounts reclassified from accumulated other comprehensive income							3.2	3.6
Net current period other comprehensive (loss) income	6.3	(0.1)	(0.4)	(0.6)	6.0	(10.7)	5.8	(5.3)
Ending balance	1,969.8	1,947.6	1,903.5	1,918.6	2,104.3	2,072.9	1,969.8	1,918.6
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	(126.3)	(126.2)	(125.8)	(102.9)	(108.9)	(98.2)	(125.8)	(98.2)
Net current period other comprehensive (loss) income	6.3	(0.1)	(0.4)	(0.6)	6.0	(10.7)
Ending balance	(120.0)	$ (126.3)	(126.2)	(103.5)	$ (102.9)	(108.9)	(120.0)	(103.5)
Foreign Currency Items
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance			(73.5)			(40.2)	(73.5)	(40.2)
Other comprehensive income (loss) before reclassifications							2.6	(8.9)
Amounts reclassified from accumulated other comprehensive income							0.0	0.0
Net current period other comprehensive (loss) income							2.6	(8.9)
Ending balance	(70.9)			(49.1)			(70.9)	(49.1)
Defined Benefit Pension Plans
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance			$ (52.3)			$ (58.0)	(52.3)	(58.0)
Other comprehensive income (loss) before reclassifications							0.0	0.0
Amounts reclassified from accumulated other comprehensive income							3.2	3.6
Net current period other comprehensive (loss) income							3.2	3.6
Ending balance	$ (49.1)			$ (54.4)			$ (49.1)	$ (54.4)

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