diff --git a/python-google-cloud-core.changes b/python-google-cloud-core.changes
index e5bef93..5656779 100644
--- a/python-google-cloud-core.changes
+++ b/python-google-cloud-core.changes
@@ -1,3 +1,8 @@
+-------------------------------------------------------------------
+Tue Mar  5 20:25:21 UTC 2024 - Robert Schweikert <rjschwei@suse.com>
+
+- Obsolete Python 3.6 build for SLE 15 SP4 and openSUSE Leap 15.4 and later
+
 -------------------------------------------------------------------
 Mon Feb 26 20:00:14 UTC 2024 - Robert Schweikert <rjschwei@suse.com>
 
diff --git a/python-google-cloud-core.spec b/python-google-cloud-core.spec
index dd81075..9ddca7d 100644
--- a/python-google-cloud-core.spec
+++ b/python-google-cloud-core.spec
@@ -37,6 +37,9 @@ Requires:       python-google-api-core >= 1.31.6
 Requires:       python-google-auth >= 1.25.0
 Recommends:     python-grpcio >= 1.38.0
 BuildArch:      noarch
+%if 0%{?sle_version} >= 150400
+Obsoletes:      python3-google-cloud-core < %{version}
+%endif
 %python_subpackages
 
 %description