Note 4 - Loans - Major Categories of Loans (Details) - USD ($)	Mar. 31, 2019	Dec. 31, 2018
Loans	$ 338,190,781	$ 343,940,842
Allowance for loan losses	2,529,209	2,509,334
Deferred origination fees net of costs	519,193	530,873
	335,142,379	340,900,635
Commercial Real Estate Portfolio Segment [Member]
Loans	236,794,302	238,834,149
Construction and Land Development [Member]
Loans	15,914,131	18,265,505
Residential Portfolio Segment [Member]
Loans	63,019,749	63,024,106
Commercial Portfolio Segment [Member]
Loans	22,095,306	23,323,073
Consumer Portfolio Segment [Member]
Loans	$ 367,293	$ 494,009

Amount of allowance to cover probable credit losses on loans and leases. Includes carryover of or adjustments to the allowance for loan losses in connection with business combinations. Excludes allowance for loans and leases covered under loss sharing agreements.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.7(d))
-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 11B
-Subparagraph (g)
-URI http://asc.fasb.org/extlink&oid=118936363&loc=SL6953423-111524

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (b)(1)(ii)
-URI http://asc.fasb.org/extlink&oid=118939070&loc=d3e15032-111544

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 11B
-Subparagraph (c)(1)
-URI http://asc.fasb.org/extlink&oid=118936363&loc=SL6953423-111524

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section S99
-Paragraph 4
-Subparagraph (SAB Topic 6.L.1)
-URI http://asc.fasb.org/extlink&oid=27010918&loc=d3e74567-122707

+ Details

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

- Definition

Amount of deferred interest and fee income, unamortized costs incurred to originate loans and leases, unamortized loan commitments and loan syndication fees, and premiums over or discounts from face amounts of acquired loans. Excludes amounts for loans and leases covered under loss sharing agreements.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.7)
-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 840
-SubTopic 30
-Section 50
-Paragraph 4
-Subparagraph (a)(4)
-URI http://asc.fasb.org/extlink&oid=84165051&loc=d3e45377-112738

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 4
-URI http://asc.fasb.org/extlink&oid=118936363&loc=d3e5074-111524

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 20
-Section 50
-Paragraph 3
-URI http://asc.fasb.org/extlink&oid=84159169&loc=d3e10152-111534

+ Details

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

- Definition

Amount before allowance of loans and leases held in portfolio, including but not limited to, commercial and consumer loans. Includes deferred interest and fees, undisbursed portion of loan balance, unamortized costs and premiums and discounts from face amounts. Excludes loans and leases covered under loss sharing agreements.

+ References

+ Details

Name:	us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount after allowance and deduction of deferred interest and fees, unamortized costs and premiums and discounts from face amounts, of loans and leases held in portfolio, including but not limited to, commercial and consumer loans. Excludes loans and leases covered under loss sharing agreements and loans held for sale.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=118952595&loc=d3e4428-111522

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.7)
-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

+ Details

Name:	us-gaap_LoansAndLeasesReceivableNetReportedAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_FinancingReceivablePortfolioSegmentAxis=us-gaap_CommercialRealEstatePortfolioSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivablePortfolioSegmentAxis=fmfg_ConstructionAndLandDevelopmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivablePortfolioSegmentAxis=us-gaap_ResidentialPortfolioSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivablePortfolioSegmentAxis=us-gaap_CommercialPortfolioSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivablePortfolioSegmentAxis=us-gaap_ConsumerPortfolioSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: