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Equity - Schedule of Matters Relating to Repurchase (Details) - Treasury Stock, Common [Member]	6 Months Ended
	Mar. 31, 2025 USD ($) shares
Schedule of Matters Relating to Repurchase [Line Items]
Number of Class A ordinary shares repurchased (Shares consolidated each 10 shares into 1 share) | shares	200,000
Total purchase price for repurchase of shares | $	$ 500

X

- Definition

Total purchase price for repurchase of shares.

+ References

No definition available.

+ Details

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Namespace Prefix:	lgcb_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Number of common shares repurchased

+ References

No definition available.

+ Details

Name:	lgcb_StockRepurchasedDuringPeriodShare
Namespace Prefix:	lgcb_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 505
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481520/505-30-50-4

+ Details

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Namespace Prefix:	srt_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: