Long-Term Debts - Schedule of Long-Term Debts (Details) - USD ($)	Sep. 30, 2024	Sep. 30, 2023
Schedule of Long-Term Debts [Line Items]
Long- term	$ 839,560	$ 1,996,326
Long- term (current portions)	$ 428,702	535,226
The Shoko Chuk in Bank [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	1.50%
Start date	May 09, 2019
End date	Apr. 25, 2024
Long- term
Long- term (current portions)		26,768
The Shoko Chukin Bank One [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	1.11%
Start date	May 26, 2020
End date	Apr. 25, 2030
Long- term	$ 96,838	113,070
Long- term (current portions)	$ 21,110	20,237
The Shoko Chukin Bank Two [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	1.50%
Start date	Feb. 04, 2022
End date	Jan. 27, 2025
Long- term		20,879
Long- term (current portions)	$ 21,780	67,456
Mizuho Bank [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	0.83%
Start date	Mar. 25, 2020
End date	Mar. 25, 2025
Long- term		6,572
Long- term (current portions)	$ 6,855	13,411
Mizuho Bank One [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	2.00%
Start date	Jun. 01, 2021
End date	Jun. 01, 2031
Long- term	$ 120,419	135,515
Long- term (current portions)	$ 20,942	20,076
Japan Finance Corporation [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	1.11%
Start date	Jul. 16, 2020
End date	Jun. 30, 2030
Long- term	$ 164,328	194,071
Long- term (current portions)	$ 38,115	36,539
Musashino Bank [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	1.50%
Start date	May 31, 2022
End date	Jun. 02, 2025
Long- term		44,489
Long- term (current portions)	$ 46,408	72,556
Japan Finance Corporation One [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	0.46%
Start date	Jun. 09, 2020
End date	Apr. 20, 2030
Long- term	$ 98,290	114,783
Long- term (current portions)	$ 21,445	20,558
Japan Finance Corporation Two [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	0.38%
Start date	Apr. 23, 2021
End date	Mar. 20, 2031
Long- term	$ 38,569	44,369
Long- term (current portions)	$ 7,714	7,395
Kiraboshi Bank One [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	0.50%
Start date	Jun. 27, 2023
End date	May 30, 2032
Long- term	$ 321,116	351,335
Long- term (current portions)	$ 45,376	43,499
Caizhi Linghang (Xiamen) Investment Management Co., Ltd [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	3.75%
Start date	Nov. 01, 2022
End date	Oct. 31, 2027
Long- term		779,879
Long- term (current portions)
Zhongli International Financial Leasing Co. LTD [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	14.56%
Start date	Aug. 11, 2022
End date	Aug. 15, 2025
Long- term		125,640
Long- term (current portions)	$ 130,625	137,061
Zhongli International Financial Leasing Co. LTD One [Member]
Schedule of Long-Term Debts [Line Items]
Annual Interest Rate	13.63%
Start date	Jul. 26, 2022
End date	Jul. 26, 2025
Long- term		65,724
Long- term (current portions)	$ 68,332	$ 69,670
Pledge		Vehicle

Long term debt pledge.

No definition available.

Name:	lgcb_LongTermDebtPledge
Namespace Prefix:	lgcb_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	instant

- Definition

Start date of long-term debt.

+ References

No definition available.

+ Details

Name:	lgcb_LongTermDebtStartDate
Namespace Prefix:	lgcb_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount, after deduction of unamortized premium (discount) and debt issuance cost, of long-term debt classified as current. Excludes lease obligation.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_LongTermDebtCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Maturity date of long-term debt, in YYYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_LongTermDebtMaturityDate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount, after deduction of unamortized premium (discount) and debt issuance cost, of long-term debt classified as noncurrent. Excludes lease obligation.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_LongTermDebtNoncurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The interest rate applicable to the portion of the carrying amount of long-term borrowings outstanding as of the balance sheet date, including current maturities, which accrues interest at a set, unchanging rate.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22)(a)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_LongTermDebtPercentageBearingFixedInterestRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- 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

No definition available.

+ Details

Name:	us-gaap_ScheduleOfCapitalizationLongtermDebtLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_TheShokoChukInBankMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_TheShokoChukinBankOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_TheShokoChukinBankTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_MizuhoBankMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_MizuhoBankOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_JapanFinanceCorporationMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_MusashinoBankMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_JapanFinanceCorporationOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_JapanFinanceCorporationTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_KiraboshiBankOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_CaizhiLinghangXiamenInvestmentManagementCoLtdMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_ZhongliInternationalFinancialLeasingCoLTDMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lgcb_ZhongliInternationalFinancialLeasingCoLTDOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: