I found myself looking this up, and it might be useful, so! All full moons during Remus' Hogwarts years.
First Year (1971-1972)
September 5
October 4
November 2
December 2
December 31
January 30
February 29
March 29
April 28
May 28
June 26
July 26
August 24
Second Year (1972-1973)
September 23
October 22
November 20
December 20
January 18
February 17
March 18
April 17
May 17
June 15
Jul 15
August 14
Third Year (1973-1974)
September 12
October 12
November 10
December 10
January 8
February 6
March 8
April 6
May 6
June 4
July 4
August 3
Fourth Year (1974-1975)
September 1
October 1
October 31
November 29
December 29
January 27
February 26
March 27
April 25
May 25
June 23
July 23
August 21
Fifth Year (1975-1976)
Septeber 20
October 20
November 18
December 18
January 17
February 15
March 16
April 14
May 13
June 12
July 11
August 9
Sixth Year (1976-1977)
September 8
October 8
November 6
December 6
January 5
February 4
March 5
April 4
May 3
June 1
July 1
July 30
August 28
Seventh Year (1977-1978)
September 27
October 26
November 25
December 25
January 24
February 23
March 24
April 23
May 22
June 20
And a
useful website for any other year this info is needed for.