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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, 2022
Aug. 31, 2021
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Amounts recognized in the consolidated balance sheets consist of:          
Non-current assets $ 8.0 $ 13.0 $ 8.0 $ 13.0  
Non-current liabilities $ (41.4) $ (60.2) $ (41.4) $ (60.2)  
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     $ 224.7 $ 249.6  
Service cost     4.4 4.6 $ 4.3
Interest cost     5.3 5.3 6.4
Actuarial (gains) losses     (43.1) (5.2)  
Benefits paid     (15.3) (29.6)  
Other     0.0 0.0  
Benefit obligation at end of year $ 176.0 $ 224.7 176.0 224.7 249.6
Change in plan assets:          
Fair value of plan assets at beginning of year     182.6 167.1  
Actual return on plan assets     (33.6) 21.7  
Employer contributions     7.8 23.4  
Benefits paid     (15.3) (29.6)  
Other     0.0 0.0  
Fair value of plan assets at end of year 141.5 182.6 141.5 182.6 167.1
Funded status at end of year:          
Funded status at the end of year (34.5) (42.1) (34.5) (42.1)  
Amounts recognized in the consolidated balance sheets consist of:          
Non-current assets 7.6 13.0 7.6 13.0  
Current liabilities (3.9) (5.2) (3.9) (5.2)  
Non-current liabilities (38.2) (49.9) (38.2) (49.9)  
Net amount recognized in consolidated balance sheets (34.5) (42.1) (34.5) (42.1)  
Accumulated benefit obligation 175.3 223.8 175.3 223.8  
Pre-tax amounts in accumulated other comprehensive loss:          
Prior service cost (2.7) (5.6) (2.7) (5.6)  
Net actuarial loss (54.2) (55.2) (54.2) (55.2)  
Amounts in accumulated other comprehensive loss (56.9) (60.8) (56.9) (60.8)  
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 42.1 81.7 42.1 81.7  
Accumulated benefit obligation 41.4 80.8 41.4 80.8  
Plan assets 0.0 26.6 0.0 26.6  
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 133.9 143.0 133.9 143.0  
Accumulated benefit obligation 133.9 143.0 133.9 143.0  
Plan assets 141.5 156.0 141.5 156.0  
Pension Plan | International Plans          
Change in benefit obligation:          
Benefit obligation at beginning of year     52.6 49.2  
Service cost     0.4 0.3 0.3
Interest cost     0.9 0.9 0.9
Actuarial (gains) losses     (17.1) 1.7  
Benefits paid     (2.1) (1.3)  
Other     (3.2) 1.8  
Benefit obligation at end of year 31.5 52.6 31.5 52.6 49.2
Change in plan assets:          
Fair value of plan assets at beginning of year     42.2 35.1  
Actual return on plan assets     (11.6) 5.3  
Employer contributions     3.0 2.1  
Benefits paid     (2.1) (1.3)  
Other     (3.0) 1.0  
Fair value of plan assets at end of year 28.5 42.2 28.5 42.2 $ 35.1
Funded status at end of year:          
Funded status at the end of year (3.0) (10.4) (3.0) (10.4)  
Amounts recognized in the consolidated balance sheets consist of:          
Non-current assets 0.4 0.0 0.4 0.0  
Current liabilities (0.2) (0.1) (0.2) (0.1)  
Non-current liabilities (3.2) (10.3) (3.2) (10.3)  
Net amount recognized in consolidated balance sheets (3.0) (10.4) (3.0) (10.4)  
Accumulated benefit obligation 31.3 51.7 31.3 51.7  
Pre-tax amounts in accumulated other comprehensive loss:          
Prior service cost (0.1) (0.1) (0.1) (0.1)  
Net actuarial loss (6.5) (11.3) (6.5) (11.3)  
Amounts in accumulated other comprehensive loss (6.6) (11.4) (6.6) (11.4)  
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 3.4 52.6 3.4 52.6  
Accumulated benefit obligation 2.3 51.7 2.3 51.7  
Plan assets 0.0 42.2 0.0 42.2  
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 28.1 0.0 28.1 0.0  
Accumulated benefit obligation 29.0 0.0 29.0 0.0  
Plan assets $ 28.5 $ 0.0 $ 28.5 $ 0.0