diff --git a/drake_cmake_external/CMakeLists.txt b/drake_cmake_external/CMakeLists.txt
index b74794ba..2244f821 100644
--- a/drake_cmake_external/CMakeLists.txt
+++ b/drake_cmake_external/CMakeLists.txt
@@ -24,8 +24,6 @@ endif()
 
 list(APPEND CMAKE_PREFIX_PATH "${CMAKE_INSTALL_PREFIX}")
 
-find_package(Python3 REQUIRED COMPONENTS Interpreter Development)
-
 include(ExternalProject)
 
 # This shows how to fetch Eigen from source as part of Drake's CMake build.
diff --git a/drake_cmake_external/drake_external_examples/CMakeLists.txt b/drake_cmake_external/drake_external_examples/CMakeLists.txt
index 50aefc9a..681a961d 100644
--- a/drake_cmake_external/drake_external_examples/CMakeLists.txt
+++ b/drake_cmake_external/drake_external_examples/CMakeLists.txt
@@ -1,22 +1,29 @@
 # SPDX-License-Identifier: MIT-0
 
-cmake_minimum_required(VERSION 3.10.2)
+cmake_minimum_required(VERSION 3.16)
 project(drake_external_examples)
 
-include(CTest)
-
-if(APPLE)
-  set(FIND_PYTHON_INTERP_VERSION 3.12)
-else()
-  set(FIND_PYTHON_INTERP_VERSION 3.6)
-endif()
-find_package(PythonInterp ${FIND_PYTHON_INTERP_VERSION} MODULE REQUIRED)
-
 find_package(drake CONFIG REQUIRED)
 
-get_filename_component(PYTHONPATH
-  "${drake_DIR}/../../python${PYTHON_VERSION_MAJOR}.${PYTHON_VERSION_MINOR}/site-packages"
+find_package(Python3 ${drake_PYTHON_VERSION} EXACT REQUIRED COMPONENTS Interpreter Development)
+
+get_filename_component(DRAKE_PYTHONPATH
+  "${drake_DIR}/../../python${drake_PYTHON_VERSION}/site-packages"
   REALPATH
 )
 
-add_subdirectory(apps)
+add_executable(simple_continuous_time_system simple_continuous_time_system.cc)
+target_link_libraries(simple_continuous_time_system drake::drake)
+
+include(CTest)
+
+add_test(NAME simple_continuous_time_system
+  COMMAND simple_continuous_time_system
+)
+add_test(NAME import_all_test COMMAND
+  "${Python3_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/import_all_test.py"
+)
+set_tests_properties(import_all_test PROPERTIES
+  ENVIRONMENT "PYTHONPATH=${DRAKE_PYTHONPATH}"
+)
+
diff --git a/drake_cmake_external/drake_external_examples/apps/CMakeLists.txt b/drake_cmake_external/drake_external_examples/apps/CMakeLists.txt
deleted file mode 100644
index 053a60b6..00000000
--- a/drake_cmake_external/drake_external_examples/apps/CMakeLists.txt
+++ /dev/null
@@ -1,14 +0,0 @@
-# SPDX-License-Identifier: MIT-0
-
-add_executable(simple_continuous_time_system simple_continuous_time_system.cc)
-target_link_libraries(simple_continuous_time_system drake::drake)
-add_test(NAME simple_continuous_time_system
-  COMMAND simple_continuous_time_system
-)
-
-add_test(NAME import_all_test COMMAND
-  "${PYTHON_EXECUTABLE}" "${CMAKE_CURRENT_SOURCE_DIR}/import_all_test.py"
-)
-set_tests_properties(import_all_test PROPERTIES
-  ENVIRONMENT "PYTHONPATH=${PYTHONPATH}"
-)
diff --git a/drake_cmake_external/drake_external_examples/apps/import_all_test.py b/drake_cmake_external/drake_external_examples/import_all_test.py
similarity index 100%
rename from drake_cmake_external/drake_external_examples/apps/import_all_test.py
rename to drake_cmake_external/drake_external_examples/import_all_test.py
diff --git a/drake_cmake_external/drake_external_examples/apps/simple_continuous_time_system.cc b/drake_cmake_external/drake_external_examples/simple_continuous_time_system.cc
similarity index 100%
rename from drake_cmake_external/drake_external_examples/apps/simple_continuous_time_system.cc
rename to drake_cmake_external/drake_external_examples/simple_continuous_time_system.cc
diff --git a/drake_cmake_installed_apt/CMakeLists.txt b/drake_cmake_installed_apt/CMakeLists.txt
index 77906c94..7661e4d8 100644
--- a/drake_cmake_installed_apt/CMakeLists.txt
+++ b/drake_cmake_installed_apt/CMakeLists.txt
@@ -1,6 +1,6 @@
 # SPDX-License-Identifier: MIT-0
 
-cmake_minimum_required(VERSION 3.10)
+cmake_minimum_required(VERSION 3.16)
 project(drake_cmake_installed_apt)
 
 include(CTest)
@@ -21,23 +21,13 @@ target_include_directories(gtest PUBLIC
 )
 target_link_libraries(gtest Threads::Threads)
 
-if(CMAKE_VERSION VERSION_LESS 3.12)
-  list(INSERT CMAKE_MODULE_PATH 0
-    "${CMAKE_CURRENT_SOURCE_DIR}/third_party/cmake/3.12/Modules"
-  )
-endif()
-
-find_package(Python 3.6 MODULE REQUIRED)
-set(PYTHON_VERSION_MAJOR_MINOR
-  "${Python_VERSION_MAJOR}.${Python_VERSION_MINOR}"
-)
-
 find_package(drake CONFIG REQUIRED PATHS /opt/drake)
+find_package(Python3 ${drake_PYTHON_VERSION} EXACT REQUIRED COMPONENTS Interpreter Development)
 
 get_filename_component(DRAKE_PYTHONPATH "${drake_DIR}" DIRECTORY)
 get_filename_component(DRAKE_PYTHONPATH "${DRAKE_PYTHONPATH}" DIRECTORY)
 set(DRAKE_PYTHONPATH
-  "${DRAKE_PYTHONPATH}/python${PYTHON_VERSION_MAJOR_MINOR}/site-packages"
+  "${DRAKE_PYTHONPATH}/python${drake_PYTHON_VERSION}/site-packages"
 )
 
 add_subdirectory(src)
diff --git a/drake_cmake_installed_apt/src/CMakeLists.txt b/drake_cmake_installed_apt/src/CMakeLists.txt
index 3bcfc541..13a012eb 100644
--- a/drake_cmake_installed_apt/src/CMakeLists.txt
+++ b/drake_cmake_installed_apt/src/CMakeLists.txt
@@ -9,7 +9,7 @@ add_test(NAME cc_particle_test COMMAND particle_test)
 set_tests_properties(cc_particle_test PROPERTIES LABELS small TIMEOUT 60)
 
 add_test(NAME python_particle_test
-  COMMAND Python::Interpreter -B -m unittest particle_test
+  COMMAND Python3::Interpreter -B -m unittest particle_test
 )
 set_tests_properties(python_particle_test PROPERTIES
   ENVIRONMENT "PYTHONPATH=${DRAKE_PYTHONPATH}"