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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, 2022
Aug. 31, 2021
Aug. 31, 2020
Domestic Plans      
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) [Abstract]      
Service cost $ 4.4 $ 4.6 $ 4.3
Interest cost 5.3 5.3 6.4
Expected return on plan assets (11.2) (11.0) (10.4)
Amortization of prior service cost 2.9 2.9 4.0
Settlement 0.4 3.9 0.0
Recognized actuarial loss 2.4 4.1 4.2
Net periodic pension cost $ 4.2 $ 9.8 $ 8.5
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Benefit Obligation [Abstract]      
Discount rate 4.40% 2.40%  
Rate of compensation increase 5.00% 5.00%  
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate 2.40% 2.20% 2.80%
Expected return on plan assets 6.30% 6.80% 7.00%
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 31.60% 41.20%  
Domestic Plans | Fixed income securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 61.20% 54.30%  
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 7.20% 4.50%  
International Plans      
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) [Abstract]      
Service cost $ 0.4 $ 0.3 $ 0.3
Interest cost 0.9 0.9 0.9
Expected return on plan assets (2.6) (2.3) (2.0)
Amortization of prior service cost 0.0 0.0 0.0
Settlement 0.0 0.0 0.0
Recognized actuarial loss 0.9 1.4 1.4
Net periodic pension cost $ (0.4) $ 0.3 $ 0.6
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Benefit Obligation [Abstract]      
Discount rate 4.90% 1.90%  
Rate of compensation increase 3.50% 3.40%  
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate 1.90% 1.90% 2.00%
Expected return on plan assets 6.40% 6.50% 6.50%
Rate of compensation increase 3.40% 3.40% 3.00%
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 16.80% 16.10%  
International Plans | Fixed income securities      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 22.80% 20.10%  
International Plans | Multi-strategy investments      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 60.40% 63.80%  
International Plans | Real estate      
Defined Benefit Plan, Plan Assets, Allocations [Abstract]      
Pension plan asset allocation, percentage 0.00% 0.00%