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v3.25.2

Condensed Financial Information of the Parent Company (Details) | 12 Months Ended
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Sep. 30, 2024
Linkage Cayman [Member] |
Condensed Financial Information of the Parent Company [Line Items] |
Percentage of consolidated net assets | 25.00%

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- References No definition available. + Details
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Namespace Prefix: | lgcb_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Percentage of consolidated net assets. + References No definition available. + Details
Name: | lgcb_PercentageOfConsolidatedNetAssets
Namespace Prefix: | lgcb_
Data Type: | dtr:percentItemType
Balance Type: | na
Period Type: | duration

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- Details
Name: | us-gaap_RelatedPartyTransactionAxis=lgcb_LinkageCaymanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |