Time expressions can be tricky to use with apostrophes. Month’s, months’, and months are in fact all correct depending on the context.
Months is used for the plural of month. month’s and months’ are used in compound time expressions. month’s is used with a singular time unit and months’ is used for a plural unit.
Month’s and months’
One month’s notice
Two months’ notice
You need to place the apostrophe before the s when you are writing about a singular time(one day, one month, one month) and after the s when it is a plural time(two days. Three months, four months)
Notice that we only need to do this when we include the noun that the time expression is about. We only do this when we can replace the apostrophe with of.(Read about when to use of in English grammar here).
One month’s free insurance
Four months’ free insurance
She is going away in one month’s time.
She is going away in two months’ time.
He was docked one month’s pay.
He was docked two months’ pay.
You can always use of if you feel like this makes things clearer:
He was docked one month of pay.
He was docked two months of pay.
In this case, months returns to a regular singular/plural noun.
If there is no noun that the time expression is connected to then months acts like a regular noun and you just need to add an s to make it plural.
I need to start work in one month.
I need to start work in two months.
Compound adjectives with month
Compound adjectives are when we combine two words with a hyphen to describe another noun.
He took a two-month holiday.
The package includes a one-month safari.
For compound adjectives, it is not necessary to add an s but it is necessary to add the hyphen.