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Nature of Operations - Additional Information (Details)
$ in Millions
8 Months Ended 12 Months Ended
Jan. 19, 2021
USD ($)
Sep. 30, 2021
USD ($)
Sep. 30, 2021
USD ($)
Segment
Sep. 30, 2020
USD ($)
Sep. 30, 2019
USD ($)
Organization Consolidation And Presentation Of Financial Statements [Line Items]          
Number of reportable segments of entity (in segments) | Segment     4    
Sales     $ 7,737.3 $ 6,856.8 $ 8,382.0
Valuation of intangible assets   $ 466.8 $ 466.8 $ 418.2  
Estimated average life     14 years 4 months 24 days 14 years 8 months 12 days  
Valuation of intangible assets with indefinite life   417.1 $ 417.1 $ 384.7  
Goodwill   1,052.0 1,052.0 1,009.5 995.7
Pratt Miller          
Organization Consolidation And Presentation Of Financial Statements [Line Items]          
Purchase price $ 111.4        
Consideration paid in cash 110.6        
Receivable for post-closing working capital adjustments 0.6        
Contingent cash consideration 1.4        
Sales of acquiree   64.3      
Valuation of intangible assets   25.6 $ 25.6    
Estimated average life     5 years 7 months 6 days    
Valuation of intangible assets with indefinite life   32.3 $ 32.3    
Goodwill $ 44.4 44.4 44.4    
Goodwill deductible for income tax purposes   $ 43.9 43.9    
Transaction costs related to acquisition     $ 1.1    
CON-E-CO          
Organization Consolidation And Presentation Of Financial Statements [Line Items]          
Sales       $ 35.0 $ 32.7