Share-Based Compensation Share-Based Compensation (Details) - USD ($)	9 Months Ended
	Dec. 31, 2021	Dec. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Item]
Remaining shares available for grant	3,139,888
Weighted-average assumptions used for options granted:
Risk-free interest rate	1.10%	0.46%
Expected life of options	5 years 10 months 24 days	6 years
Exptected dividend yield of stock	0.95%	0.96%
Expected volatility of stock	24.27%	23.04%
Estimated forfeiture rate	2.85%	2.78%
Summary of share option activity:
Outstanding at March 31, 2017	1,637,047
Granted	284,566
Exercised	(304,341)
Forfeited	(4,043)
Outstanding at June 30, 2017	1,613,229
Exercisable at June 30, 2017	904,909
Weighted average exercise price:
Outstanding at March 31, 2017	$ 112.03
Granted	215.10
Exercised	82.95
Forfeited	128.11
Outstanding at June 30, 2017	135.66
Exercisable at June 30, 2017	$ 101.43
Average Remaining Contractual Term, Outstanding at June 30, 2017	6 years 9 months 18 days
Aggregate Intrinsic Value, Outstanding at June 30, 2017	$ 173,829,000
Average Remaining Contractual Term, Exercisable at June 30, 2017	5 years 6 months
Aggregate Intrinsic Value, Exercisable at June 30, 2017	$ 128,481,000
Non-vested stock options outstanding expected to vest	690,359
Ordinary shares, closing price	$ 243.41
Total intrinsic value of stock options exercised	$ 43,425,000	$ 36,850,000
Net cash proceeds from the exercise of stock options	$ 6,789,000	$ 26,018,000
Weighted average grant date fair value of stock option grants, per share	$ 37.52	$ 27.66
Summary of non-vested restricted share activity:
Unrecognized compensation cost related to nonvested share-based compensation granted	$ 66,715,000
Weighted Average Period For Total Compensation Expense Not Yet Recognized	2 years 2 months 12 days
Stock Appreciation Rights (SARs) [Member]
Weighted average exercise price:
FairValueOfOutstandingStockAppreciationRights		$ 491,000
Restricted Stock
Summary of non-vested restricted share activity:
Number of Restricted Shares, Non-vested at Beginning of Period	533,323
Weighted-Average Grant Date Fair Value, Non-vested at Beginning of Period	$ 121.35
Number of Restricted Shares, Granted	163,120
Weighted-Average Grant Date Fair Value, Granted	$ 197.51
Number of Restricted Shares, Vested	(174,509)
Weighted-Average Grant Date Fair Value, Vested	$ 96.30
Number of Restricted Shares, Canceled	(15,050)
Weighted-Average Grant Date Fair Value, Canceled	$ 161.59
Number of Restricted Shares, Non-vested at End of Period	506,884
Weighted-Average Grant Date Fair Value, Non-vested at End of Period	$ 155.01
Fair Value, Share-based Payment Awards, Other than Options	$ 18,267,000
Restricted Stock Units (RSUs)
Weighted average exercise price:
Weighted average grant date fair value of stock option grants, per share	$ 191.18
Summary of non-vested restricted share activity:
Number of Restricted Shares, Non-vested at Beginning of Period	29,500
Number of Restricted Shares, Granted	21,437
Number of Restricted Shares, Vested	(15,621)
Number of Restricted Shares, Canceled	(620)
Number of Restricted Shares, Non-vested at End of Period	34,696
Share-based Payment Arrangement, Expense	$ 18,861,000
Restricted Stock or Unit Expense	$ 280,402
Share-based Compensation Arrangement by Share-based Payment Award, Conversion Ratio	0.4262
Share-based Compensation Arrangement by Share-based Payment Award, Grants in Period, Weighted Average Grant Date Fair Value Attributable to Pre-Acquisition Services	$ 18,173,000
Share-based Compensation Arrangement by Share-based Payment Award, Grants in Period, Weighted Average Grant Date Fair Value	$ 53,607,000
RSUs Cantel
Summary of non-vested restricted share activity:
Number of Restricted Shares, Non-vested at Beginning of Period	0
Weighted-Average Grant Date Fair Value, Non-vested at Beginning of Period	$ 0
Number of Restricted Shares, Granted	280,402
Weighted-Average Grant Date Fair Value, Granted	$ 191.18
Number of Restricted Shares, Vested	(209,878)
Weighted-Average Grant Date Fair Value, Vested	$ 191.18
Number of Restricted Shares, Canceled	(7,602)
Weighted-Average Grant Date Fair Value, Canceled	$ 191.18
Number of Restricted Shares, Non-vested at End of Period	62,922
Weighted-Average Grant Date Fair Value, Non-vested at End of Period	$ 191.18
Unrecognized compensation cost related to nonvested share-based compensation granted	$ 9,248,000