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Pension and Defined Contribution Plans - Net Periodic Pension Cost and Pension Plan Asset Allocation (Details) - Pension Plan - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Domestic Plans      
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) [Abstract]      
Service cost $ 3.8 $ 4.4 $ 4.6
Interest cost 7.4 5.3 5.3
Expected return on plan assets (7.5) (11.2) (11.0)
Amortization of prior service cost 2.6 2.9 2.9
Settlement 0.0 0.4 3.9
Recognized actuarial loss 2.4 2.4 4.1
Net periodic pension cost $ 8.7 $ 4.2 $ 9.8
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Benefit Obligation [Abstract]      
Discount rate 5.10% 4.40%  
Rate of compensation increase 5.00% 5.00%  
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate 4.40% 2.40% 2.20%
Expected return on plan assets 5.50% 6.30% 6.80%
Rate of compensation increase 5.00% 5.00% 5.00%
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 100.00% 100.00%  
Domestic Plans | Equity securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 18.30% 31.60%  
Domestic Plans | Fixed income securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 75.00% 61.20%  
Domestic Plans | Multi-strategy investments      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 0.00% 0.00%  
Domestic Plans | Real estate      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 6.70% 7.20%  
International Plans      
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) [Abstract]      
Service cost $ 0.8 $ 0.4 $ 0.3
Interest cost 1.6 0.9 0.9
Expected return on plan assets (2.1) (2.6) (2.3)
Amortization of prior service cost 0.0 0.0 0.0
Settlement 0.0 0.0 0.0
Recognized actuarial loss 0.6 0.9 1.4
Net periodic pension cost $ 0.9 $ (0.4) $ 0.3
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Benefit Obligation [Abstract]      
Discount rate 5.90% 4.90%  
Rate of compensation increase 3.50% 3.50%  
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate 4.90% 1.90% 1.90%
Expected return on plan assets 6.40% 6.40% 6.50%
Rate of compensation increase 3.50% 3.40% 3.40%
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 100.00% 100.00%  
International Plans | Equity securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 17.60% 16.80%  
International Plans | Fixed income securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 53.30% 22.80%  
International Plans | Multi-strategy investments      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 29.10% 60.40%  
International Plans | Real estate      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 0.00% 0.00%