One stereotype of the Japanese people, true or not, is that they are overly efficient. Looking at the months of the year used in modern Japanese, it is quite easy to see where stereotypes of this sort have originated. The months are as follows, romaji first, hiragana and kanji in parenthesis.
ichigatsu (いちがつ or 一月) - January, the first month
nigatsu (にがつ or 二月) - February, the second month
sangatsu (さんがつ or 三月) - March, the third month
shigatsu (しがつ or 四月) - April, the fourth month
gogatsu (ごがつ or 五月) - May, the fifth month
rokugatsu (ろくがつ or 六月) - June, the sixth month
shichigatsu (しちがつ or 七月) - July, the seventh month
hachigatsu (はちがつ or 八月) - August, the eighth month
kugatsu (くがつ or 九月) - September, the ninth month
juugatsu (じゅうがつ or 十月) - October, the tenth month
juuichigatsu (じゅういちがつ or 十一月) - November, the eleventh month
juunigatsu (じゅうにがつ or 十二月) - December, the twelfth month
If you know your numbers, you may have recognized a pattern. The Japanese words for the months are created simply by combining the number of the month with the word "gatsu," meaning month. This makes learning the months very easy, as all you have to do is remember the order of the months, something you have likely mastered in your native language. Often, you will see the months written, for example, as 3月 instead of 三月, as Arabic numbers have become very prevalent in Japan.
The Ancient Japanese calender is not the same as the modern calender, and is actually lunar based, like many other cultures once had. As such, the words for the months in Ancient Japanese do not correspond to the same months, as the lunar year is separate from the modern Gregorian calender.