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Equity - Schedule of Matters Relating to Repurchase (Details) - Treasury Stock, Common [Member] | 6 Months Ended
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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

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- 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

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- 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

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- 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
Name: | srt_ShareRepurchaseProgramLineItems
Namespace Prefix: | srt_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Details
Name: | us-gaap_StatementEquityComponentsAxis=us-gaap_TreasuryStockCommonMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |