v3.26.1
Comprehensive Income - Schedule of Changes in Components of Accumulated Other Comprehensive (Loss) Income (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
May 31, 2026
May 31, 2025
May 31, 2026
May 31, 2025
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]        
Beginning balance $ 2,840.8 $ 2,520.4 $ 2,724.9 $ 2,378.8
Other comprehensive income before reclassifications     4.1 (1.2)
Amounts reclassified from accumulated other comprehensive loss     0.8 1.5
Other comprehensive (loss) income items, net of tax (10.9) 28.3 4.9 0.3
Ending balance 2,851.5 2,584.0 2,851.5 2,584.0
Accumulated Other Comprehensive Loss        
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]        
Beginning balance (60.7) (142.9) (76.5) (114.9)
Ending balance (71.6) (114.6) (71.6) (114.6)
Foreign Currency Items        
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]        
Beginning balance     (60.1) (70.9)
Other comprehensive income before reclassifications     4.1 (1.2)
Amounts reclassified from accumulated other comprehensive loss     0.0 0.0
Other comprehensive (loss) income items, net of tax (11.2) 27.8 4.1 (1.2)
Ending balance (56.0) (72.1) (56.0) (72.1)
Defined Benefit Pension Plans        
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]        
Beginning balance     (16.4) (44.0)
Other comprehensive income before reclassifications     0.0 0.0
Amounts reclassified from accumulated other comprehensive loss     0.8 1.5
Other comprehensive (loss) income items, net of tax 0.3 0.5 0.8 1.5
Ending balance $ (15.6) $ (42.5) $ (15.6) $ (42.5)