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Pension Plans (Details) - Pension Plan - USD ($)
$ in Millions
3 Months Ended
Nov. 30, 2022
Nov. 30, 2021
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) [Abstract]    
Service cost $ 1.1 $ 1.2
Interest cost 2.2 1.5
Expected return on plan assets (2.4) (3.4)
Amortization of prior service cost 0.7 0.7
Recognized actuarial loss 0.8 0.9
Net periodic pension cost $ 2.4 $ 0.9