diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index 2436d91690ed3..4dbaf65c9e7ab 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -361,6 +361,7 @@ Categorical
 Datetimelike
 ^^^^^^^^^^^^
 - :meth:`DatetimeIndex.map` with ``na_action="ignore"`` now works as expected. (:issue:`51644`)
+- Bug in :class:`DateOffset` which had inconsistent behavior when multiplying a :class:`DateOffset` object by a constant (:issue:`47953`)
 - Bug in :func:`date_range` when ``freq`` was a :class:`DateOffset` with ``nanoseconds`` (:issue:`46877`)
 - Bug in :meth:`Timestamp.date`, :meth:`Timestamp.isocalendar`, :meth:`Timestamp.timetuple`, and :meth:`Timestamp.toordinal` were returning incorrect results for inputs outside those supported by the Python standard library's datetime module (:issue:`53668`)
 - Bug in :meth:`Timestamp.round` with values close to the implementation bounds returning incorrect results instead of raising ``OutOfBoundsDatetime`` (:issue:`51494`)
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index 0248214d4e0a8..84b102bd4a262 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -1221,12 +1221,7 @@ cdef class RelativeDeltaOffset(BaseOffset):
                 # perform calculation in UTC
                 other = other.replace(tzinfo=None)
 
-            if self.n > 0:
-                for i in range(self.n):
-                    other = other + self._offset
-            else:
-                for i in range(-self.n):
-                    other = other - self._offset
+            other = other + (self._offset * self.n)
 
             if hasattr(self, "nanoseconds"):
                 other = self.n * Timedelta(nanoseconds=self.nanoseconds) + other
diff --git a/pandas/tests/tseries/offsets/test_offsets.py b/pandas/tests/tseries/offsets/test_offsets.py
index 6df47968bd3bb..5139331bebaf7 100644
--- a/pandas/tests/tseries/offsets/test_offsets.py
+++ b/pandas/tests/tseries/offsets/test_offsets.py
@@ -27,6 +27,7 @@
 from pandas.errors import PerformanceWarning
 
 from pandas import (
+    DataFrame,
     DatetimeIndex,
     Series,
     date_range,
@@ -1067,3 +1068,51 @@ def test_dateoffset_add_sub_timestamp_series_with_nano(offset, expected):
     assert testseries[0] == teststamp
     testseries = offset + testseries
     assert testseries[0] == expected
+
+
+@pytest.mark.parametrize(
+    "n_months, scaling_factor, start_timestamp, expected_timestamp",
+    [
+        (1, 2, "2020-01-30", "2020-03-30"),
+        (2, 1, "2020-01-30", "2020-03-30"),
+        (1, 0, "2020-01-30", "2020-01-30"),
+        (2, 0, "2020-01-30", "2020-01-30"),
+        (1, -1, "2020-01-30", "2019-12-30"),
+        (2, -1, "2020-01-30", "2019-11-30"),
+    ],
+)
+def test_offset_multiplication(
+    n_months, scaling_factor, start_timestamp, expected_timestamp
+):
+    # GH 47953
+    mo1 = DateOffset(months=n_months)
+
+    startscalar = Timestamp(start_timestamp)
+    startarray = Series([startscalar])
+
+    resultscalar = startscalar + (mo1 * scaling_factor)
+    resultarray = startarray + (mo1 * scaling_factor)
+
+    expectedscalar = Timestamp(expected_timestamp)
+    expectedarray = Series([expectedscalar])
+    assert resultscalar == expectedscalar
+
+    tm.assert_series_equal(resultarray, expectedarray)
+
+
+def test_dateoffset_operations_on_dataframes():
+    # GH 47953
+    df = DataFrame({"T": [Timestamp("2019-04-30")], "D": [DateOffset(months=1)]})
+    frameresult1 = df["T"] + 26 * df["D"]
+    df2 = DataFrame(
+        {
+            "T": [Timestamp("2019-04-30"), Timestamp("2019-04-30")],
+            "D": [DateOffset(months=1), DateOffset(months=1)],
+        }
+    )
+    expecteddate = Timestamp("2021-06-30")
+    with tm.assert_produces_warning(PerformanceWarning):
+        frameresult2 = df2["T"] + 26 * df2["D"]
+
+    assert frameresult1[0] == expecteddate
+    assert frameresult2[0] == expecteddate