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Revenue Recognition - Schedule of Revenues by Segment and Major Source (Details) - USD ($)
$ in Thousands
 3 Months Ended 9 Months Ended
May 31, 2023
May 31, 2022
May 31, 2023
May 31, 2022
Revenue from External Customer [Line Items]        
Total net sales $ 141,717 $ 123,667 $ 396,803 $ 388,399
Maintenance products        
Revenue from External Customer [Line Items]        
Total net sales 133,325 115,494 371,741 363,425
HCCP        
Revenue from External Customer [Line Items]        
Total net sales 8,392 8,173 25,062 24,974
Americas        
Revenue from External Customer [Line Items]        
Total net sales 71,130 61,453 192,034 172,238
Americas | Maintenance products        
Revenue from External Customer [Line Items]        
Total net sales 67,435 57,778 180,132 160,171
Americas | HCCP        
Revenue from External Customer [Line Items]        
Total net sales 3,695 3,675 11,902 12,067
EMEA        
Revenue from External Customer [Line Items]        
Total net sales 52,524 49,450 140,105 161,068
EMEA | Maintenance products        
Revenue from External Customer [Line Items]        
Total net sales 49,721 47,289 132,801 154,825
EMEA | HCCP        
Revenue from External Customer [Line Items]        
Total net sales 2,803 2,161 7,304 6,243
Asia-Pacific        
Revenue from External Customer [Line Items]        
Total net sales 18,063 12,764 64,664 55,093
Asia-Pacific | Maintenance products        
Revenue from External Customer [Line Items]        
Total net sales 16,169 10,427 58,808 48,429
Asia-Pacific | HCCP        
Revenue from External Customer [Line Items]        
Total net sales $ 1,894 $ 2,337 $ 5,856 $ 6,664