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Pension and Defined Contribution Plans - Net Periodic Pension Cost and Pension Plan Asset Allocation (Details) - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2024
Aug. 31, 2023
Aug. 31, 2022
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Defined Benefit Plan, Net Periodic Benefit (Cost) Credit, Settlement Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration] Other Nonoperating Income (Expense) Other Nonoperating Income (Expense)  
Domestic Plans | Pension Plan      
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) [Abstract]      
Service cost $ 3.6 $ 3.8 $ 4.4
Interest cost 7.8 7.4 5.3
Expected return on plan assets (6.7) (7.5) (11.2)
Amortization of prior service cost 0.1 2.6 2.9
Settlement 0.0 0.0 0.4
Recognized actuarial loss 1.7 2.4 2.4
Net periodic pension cost $ 6.5 $ 8.7 $ 4.2
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Benefit Obligation [Abstract]      
Discount rate 4.90% 5.10%  
Rate of compensation increase 5.00% 5.00%  
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate 5.10% 4.40% 2.40%
Expected return on plan assets 5.30% 5.50% 6.30%
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 | Pension Plan | Equity securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 17.20% 18.30%  
Domestic Plans | Pension Plan | Fixed income securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 77.30% 75.00%  
Domestic Plans | Pension Plan | Multi-strategy investments      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 0.00% 0.00%  
Domestic Plans | Pension Plan | Real estate      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 5.50% 6.70%  
International Plans | Pension Plan      
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) [Abstract]      
Service cost $ 0.9 $ 0.8 $ 0.4
Interest cost 2.0 1.6 0.9
Expected return on plan assets (2.0) (2.1) (2.6)
Amortization of prior service cost 0.0 0.0 0.0
Settlement 0.0 0.0 0.0
Recognized actuarial loss 1.6 0.6 0.9
Net periodic pension cost $ 2.5 $ 0.9 $ (0.4)
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Benefit Obligation [Abstract]      
Discount rate 5.90% 5.90%  
Rate of compensation increase 3.40% 3.50%  
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate 5.90% 4.90% 1.90%
Expected return on plan assets 4.70% 6.40% 6.40%
Rate of compensation increase 3.50% 3.50% 3.40%
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 100.00% 100.00%  
International Plans | Pension Plan | Equity securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 0.00% 17.60%  
International Plans | Pension Plan | Fixed income securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 93.20% 53.30%  
International Plans | Pension Plan | Multi-strategy investments      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 6.80% 29.10%  
International Plans | Pension Plan | Real estate      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 0.00% 0.00%