Note 10 - Retirement Plans (Details Textual)	3 Months Ended
Mar. 31, 2022 USD ($)	Mar. 31, 2021 USD ($)
Defined Contribution Plan, Employer Discretionary Contribution Amount	$ 79,740	$ 76,924
Number of Employees Covered by Life Insurance Policy	12
Other Postretirement Benefits Cost (Reversal of Cost)	$ 1,702	1,661
Employee Benefits and Share-Based Compensation	$ 511,792	472,888
Supplemental Employee Retirement Plan [Member]
Number of Employees Participating in Plan	3
Employee Benefits and Share-Based Compensation	$ 45,000	$ 42,000
Profit Sharing Plan [Member]
Defined Contribution Plan, Employer Matching Contribution, Percent of Match	4.00%
Defined Contribution Plan, Employers Matching Contribution, Annual Vesting Percentage	100.00%

Number of employees provided with certain life insurance benefits.

No definition available.

Name:	fmfg_NumberOfEmployeesCoveredByLifeInsurancePolicy
Namespace Prefix:	fmfg_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

Number of employees participating in the plan.

No definition available.

Name:	fmfg_NumberOfEmployeesParticipatingInPlan
Namespace Prefix:	fmfg_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

Amount of discretionary contributions made by an employer to a defined contribution plan.

No definition available.

Name:	us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

Percentage employer matches of the employee's percentage contribution matched.

No definition available.

Name:	us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

Percentage of employer's matching contributions to a defined contribution plan that vests in a given year.

No definition available.

Name:	us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

Amount of expense for employee benefit and equity-based compensation.

No definition available.

Name:	us-gaap_EmployeeBenefitsAndShareBasedCompensation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

Amount of cost (reversal of cost) for other postretirement benefits. Excludes pension benefits.

No definition available.

Name:	us-gaap_OtherPostretirementBenefitExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

Name:	us-gaap_RetirementPlanTypeAxis=us-gaap_SupplementalEmployeeRetirementPlanDefinedBenefitMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_RetirementPlanNameAxis=fmfg_ProfitSharingPlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: