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Pension and Defined Contribution Plans - Domestic and International Pension Plans (Details) - USD ($)
$ in Millions
 3 Months Ended 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Amounts recognized in the consolidated balance sheets consist of:          
Non-current assets $ 12.4 $ 8.0 $ 12.4 $ 8.0  
Non-current liabilities $ (38.4) $ (41.4) $ (38.4) $ (41.4)  
Pensions plans in which plan assets exceed benefit obligation:          
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) Excluding Service Cost, Statement of Income or Comprehensive Income [Extensible Enumeration] Cost of Goods and Services Sold, Selling, General and Administrative Expense Cost of Goods and Services Sold, Selling, General and Administrative Expense Cost of Goods and Services Sold, Selling, General and Administrative Expense Cost of Goods and Services Sold, Selling, General and Administrative Expense  
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) Other Nonoperating Income (Expense) Other Nonoperating Income (Expense)  
Pension Plan | Domestic Plans          
Change in benefit obligation:          
Benefit obligation at beginning of year     $ 176.0 $ 224.7  
Service cost     3.8 4.4 $ 4.6
Interest cost     7.4 5.3 5.3
Actuarial gains     (16.2) (43.1)  
Benefits paid     (11.2) (15.3)  
Other     0.0 0.0  
Benefit obligation at end of year $ 159.8 $ 176.0 159.8 176.0 224.7
Change in plan assets:          
Fair value of plan assets at beginning of year     141.5 182.6  
Actual return on plan assets     (1.3) (33.6)  
Employer contributions     3.7 7.8  
Benefits paid     (11.2) (15.3)  
Other     0.0 0.0  
Fair value of plan assets at end of year 132.7 141.5 132.7 141.5 182.6
Funded status at end of year:          
Funded status at the end of year (27.1) (34.5) (27.1) (34.5)  
Amounts recognized in the consolidated balance sheets consist of:          
Non-current assets 10.1 7.6 10.1 7.6  
Current liabilities (3.4) (3.9) (3.4) (3.9)  
Non-current liabilities (33.8) (38.2) (33.8) (38.2)  
Net amount recognized in consolidated balance sheets (27.1) (34.5) (27.1) (34.5)  
Accumulated benefit obligation 158.9 175.3 158.9 175.3  
Pre-tax amounts in accumulated other comprehensive loss:          
Prior service cost (0.1) (2.7) (0.1) (2.7)  
Net actuarial loss (44.3) (54.2) (44.3) (54.2)  
Amounts in accumulated other comprehensive loss (44.4) (56.9) (44.4) (56.9)  
Pension Plan | Domestic Plans | Pensions plans in which benefit obligation exceeds plan assets:          
Pensions plans in which benefit obligation exceeds plan assets:          
Projected benefit obligation 37.2 42.1 37.2 42.1  
Accumulated benefit obligation 36.3 41.4 36.3 41.4  
Plan assets 0.0 0.0 0.0 0.0  
Pension Plan | Domestic Plans | Pensions plans in which plan assets exceed benefit obligation:          
Pensions plans in which plan assets exceed benefit obligation:          
Projected benefit obligation 122.6 133.9 122.6 133.9  
Accumulated benefit obligation 122.6 133.9 122.6 133.9  
Plan assets 132.7 141.5 132.7 141.5  
Pension Plan | International Plans          
Change in benefit obligation:          
Benefit obligation at beginning of year     31.5 52.6  
Service cost     0.8 0.4 0.3
Interest cost     1.6 0.9 0.9
Actuarial gains     (1.2) (17.1)  
Benefits paid     (1.9) (2.1)  
Other     3.8 (3.2)  
Benefit obligation at end of year 34.6 31.5 34.6 31.5 52.6
Change in plan assets:          
Fair value of plan assets at beginning of year     28.5 42.2  
Actual return on plan assets     (5.2) (11.6)  
Employer contributions     7.9 3.0  
Benefits paid     (1.9) (2.1)  
Other     2.8 (3.0)  
Fair value of plan assets at end of year 32.1 28.5 32.1 28.5 $ 42.2
Funded status at end of year:          
Funded status at the end of year (2.5) (3.0) (2.5) (3.0)  
Amounts recognized in the consolidated balance sheets consist of:          
Non-current assets 2.3 0.4 2.3 0.4  
Current liabilities (0.2) (0.2) (0.2) (0.2)  
Non-current liabilities (4.6) (3.2) (4.6) (3.2)  
Net amount recognized in consolidated balance sheets (2.5) (3.0) (2.5) (3.0)  
Accumulated benefit obligation 31.9 31.3 31.9 31.3  
Pre-tax amounts in accumulated other comprehensive loss:          
Prior service cost (0.1) (0.1) (0.1) (0.1)  
Net actuarial loss (13.4) (6.5) (13.4) (6.5)  
Amounts in accumulated other comprehensive loss (13.5) (6.6) (13.5) (6.6)  
Pension Plan | International Plans | Pensions plans in which benefit obligation exceeds plan assets:          
Pensions plans in which benefit obligation exceeds plan assets:          
Projected benefit obligation 5.6 3.4 5.6 3.4  
Accumulated benefit obligation 3.5 2.3 3.5 2.3  
Plan assets 0.8 0.0 0.8 0.0  
Pension Plan | International Plans | Pensions plans in which plan assets exceed benefit obligation:          
Pensions plans in which plan assets exceed benefit obligation:          
Projected benefit obligation 29.0 28.1 29.0 28.1  
Accumulated benefit obligation 28.4 29.0 28.4 29.0  
Plan assets $ 31.3 $ 28.5 $ 31.3 $ 28.5