diff --git a/src/flint/test/test_all.py b/src/flint/test/test_all.py
index 3d64e712..66dba04c 100644
--- a/src/flint/test/test_all.py
+++ b/src/flint/test/test_all.py
@@ -841,6 +841,10 @@ def test_fmpq():
     assert raises(lambda: Q(1,2) / Q(0), ZeroDivisionError)
     assert raises(lambda: Q(1,2) / 0, ZeroDivisionError)
 
+    assert Q(2,3).gcd(Q(4,9)) == Q(2,9)
+    assert Q(2,3).gcd(5) == Q(1,3)
+    assert raises(lambda: Q(2,3).gcd([]), TypeError)
+
     assert Q(5,3).floor() == flint.fmpz(1)
     assert Q(-5,3).floor() == flint.fmpz(-2)
     assert Q(5,3).ceil() == flint.fmpz(2)
diff --git a/src/flint/types/fmpq.pyx b/src/flint/types/fmpq.pyx
index 4481f20f..6f64f85d 100644
--- a/src/flint/types/fmpq.pyx
+++ b/src/flint/types/fmpq.pyx
@@ -288,6 +288,24 @@ cdef class fmpq(flint_scalar):
     def __rtruediv__(s, t):
         return fmpq._div_(t, s)
 
+    def gcd(s, t):
+        """GCD of two rational numbers.
+
+            >>> fmpq(1,2).gcd(fmpq(3,4))
+            1/4
+
+        The GCD is defined as the GCD of the numerators divided by the LCM of
+        the denominators. This is consistent with ``fmpz.gcd()`` but not with
+        ``fmpq_poly.gcd()``.
+        """
+        cdef fmpq r
+        t = any_as_fmpq(t)
+        if t is NotImplemented:
+            raise TypeError("fmpq expected")
+        r = fmpq.__new__(fmpq)
+        fmpq_gcd(r.val, (<fmpq>s).val, (<fmpq>t).val)
+        return r
+
     def next(s, bint signed=True, bint minimal=True):
         """
         Returns the next rational number after *s* as ordered by