diff --git a/tests/Integration/Database/EloquentModelLoadMaxTest.php b/tests/Integration/Database/EloquentModelLoadMaxTest.php
new file mode 100644
index 000000000000..cf6a5d7bd8c7
--- /dev/null
+++ b/tests/Integration/Database/EloquentModelLoadMaxTest.php
@@ -0,0 +1,104 @@
+<?php
+
+namespace Illuminate\Tests\Integration\Database\EloquentModelLoadMaxTest;
+
+use Illuminate\Database\Eloquent\Model;
+use Illuminate\Database\Schema\Blueprint;
+use Illuminate\Support\Facades\DB;
+use Illuminate\Support\Facades\Schema;
+use Illuminate\Tests\Integration\Database\DatabaseTestCase;
+
+class EloquentModelLoadMaxTest extends DatabaseTestCase
+{
+    protected function afterRefreshingDatabase()
+    {
+        Schema::create('base_models', function (Blueprint $table) {
+            $table->increments('id');
+        });
+
+        Schema::create('related1s', function (Blueprint $table) {
+            $table->increments('id');
+            $table->unsignedInteger('base_model_id');
+            $table->integer('number');
+        });
+
+        Schema::create('related2s', function (Blueprint $table) {
+            $table->increments('id');
+            $table->unsignedInteger('base_model_id');
+            $table->integer('number');
+        });
+
+        BaseModel::create();
+
+        Related1::create(['base_model_id' => 1, 'number' => 10]);
+        Related1::create(['base_model_id' => 1, 'number' => 11]);
+        Related2::create(['base_model_id' => 1, 'number' => 12]);
+        Related2::create(['base_model_id' => 1, 'number' => 13]);
+    }
+
+    public function testLoadMaxSingleRelation()
+    {
+        $model = BaseModel::first();
+
+        DB::enableQueryLog();
+
+        $model->loadMax('related1', 'number');
+
+        $this->assertCount(1, DB::getQueryLog());
+        $this->assertEquals(11, $model->related1_max_number);
+    }
+
+    public function testLoadMaxMultipleRelations()
+    {
+        $model = BaseModel::first();
+
+        DB::enableQueryLog();
+
+        $model->loadMax(['related1', 'related2'], 'number');
+
+        $this->assertCount(1, DB::getQueryLog());
+        $this->assertEquals(11, $model->related1_max_number);
+        $this->assertEquals(13, $model->related2_max_number);
+    }
+}
+
+class BaseModel extends Model
+{
+    public $timestamps = false;
+
+    protected $guarded = [];
+
+    public function related1()
+    {
+        return $this->hasMany(Related1::class);
+    }
+
+    public function related2()
+    {
+        return $this->hasMany(Related2::class);
+    }
+}
+
+class Related1 extends Model
+{
+    public $timestamps = false;
+
+    protected $fillable = ['base_model_id', 'number'];
+
+    public function parent()
+    {
+        return $this->belongsTo(BaseModel::class);
+    }
+}
+
+class Related2 extends Model
+{
+    public $timestamps = false;
+
+    protected $fillable = ['base_model_id', 'number'];
+
+    public function parent()
+    {
+        return $this->belongsTo(BaseModel::class);
+    }
+}
diff --git a/tests/Integration/Database/EloquentModelLoadMinTest.php b/tests/Integration/Database/EloquentModelLoadMinTest.php
new file mode 100644
index 000000000000..b63e2ec2dc47
--- /dev/null
+++ b/tests/Integration/Database/EloquentModelLoadMinTest.php
@@ -0,0 +1,104 @@
+<?php
+
+namespace Illuminate\Tests\Integration\Database\EloquentModelLoadMinTest;
+
+use Illuminate\Database\Eloquent\Model;
+use Illuminate\Database\Schema\Blueprint;
+use Illuminate\Support\Facades\DB;
+use Illuminate\Support\Facades\Schema;
+use Illuminate\Tests\Integration\Database\DatabaseTestCase;
+
+class EloquentModelLoadMinTest extends DatabaseTestCase
+{
+    protected function afterRefreshingDatabase()
+    {
+        Schema::create('base_models', function (Blueprint $table) {
+            $table->increments('id');
+        });
+
+        Schema::create('related1s', function (Blueprint $table) {
+            $table->increments('id');
+            $table->unsignedInteger('base_model_id');
+            $table->integer('number');
+        });
+
+        Schema::create('related2s', function (Blueprint $table) {
+            $table->increments('id');
+            $table->unsignedInteger('base_model_id');
+            $table->integer('number');
+        });
+
+        BaseModel::create();
+
+        Related1::create(['base_model_id' => 1, 'number' => 10]);
+        Related1::create(['base_model_id' => 1, 'number' => 11]);
+        Related2::create(['base_model_id' => 1, 'number' => 12]);
+        Related2::create(['base_model_id' => 1, 'number' => 13]);
+    }
+
+    public function testLoadMinSingleRelation()
+    {
+        $model = BaseModel::first();
+
+        DB::enableQueryLog();
+
+        $model->loadMin('related1', 'number');
+
+        $this->assertCount(1, DB::getQueryLog());
+        $this->assertEquals(10, $model->related1_min_number);
+    }
+
+    public function testLoadMinMultipleRelations()
+    {
+        $model = BaseModel::first();
+
+        DB::enableQueryLog();
+
+        $model->loadMin(['related1', 'related2'], 'number');
+
+        $this->assertCount(1, DB::getQueryLog());
+        $this->assertEquals(10, $model->related1_min_number);
+        $this->assertEquals(12, $model->related2_min_number);
+    }
+}
+
+class BaseModel extends Model
+{
+    public $timestamps = false;
+
+    protected $guarded = [];
+
+    public function related1()
+    {
+        return $this->hasMany(Related1::class);
+    }
+
+    public function related2()
+    {
+        return $this->hasMany(Related2::class);
+    }
+}
+
+class Related1 extends Model
+{
+    public $timestamps = false;
+
+    protected $fillable = ['base_model_id', 'number'];
+
+    public function parent()
+    {
+        return $this->belongsTo(BaseModel::class);
+    }
+}
+
+class Related2 extends Model
+{
+    public $timestamps = false;
+
+    protected $fillable = ['base_model_id', 'number'];
+
+    public function parent()
+    {
+        return $this->belongsTo(BaseModel::class);
+    }
+}
diff --git a/tests/Integration/Database/EloquentModelLoadSumTest.php b/tests/Integration/Database/EloquentModelLoadSumTest.php
new file mode 100644
index 000000000000..0e4e5fa84b8d
--- /dev/null
+++ b/tests/Integration/Database/EloquentModelLoadSumTest.php
@@ -0,0 +1,103 @@
+<?php
+
+namespace Illuminate\Tests\Integration\Database\EloquentModelLoadSumTest;
+
+use Illuminate\Database\Eloquent\Model;
+use Illuminate\Database\Schema\Blueprint;
+use Illuminate\Support\Facades\DB;
+use Illuminate\Support\Facades\Schema;
+use Illuminate\Tests\Integration\Database\DatabaseTestCase;
+
+class EloquentModelLoadSumTest extends DatabaseTestCase
+{
+    protected function afterRefreshingDatabase()
+    {
+        Schema::create('base_models', function (Blueprint $table) {
+            $table->increments('id');
+        });
+
+        Schema::create('related1s', function (Blueprint $table) {
+            $table->increments('id');
+            $table->unsignedInteger('base_model_id');
+            $table->integer('number');
+        });
+
+        Schema::create('related2s', function (Blueprint $table) {
+            $table->increments('id');
+            $table->unsignedInteger('base_model_id');
+            $table->integer('number');
+        });
+
+        BaseModel::create();
+
+        Related1::create(['base_model_id' => 1, 'number' => 10]);
+        Related1::create(['base_model_id' => 1, 'number' => 11]);
+        Related2::create(['base_model_id' => 1, 'number' => 12]);
+    }
+
+    public function testLoadSumSingleRelation()
+    {
+        $model = BaseModel::first();
+
+        DB::enableQueryLog();
+
+        $model->loadSum('related1', 'number');
+
+        $this->assertCount(1, DB::getQueryLog());
+        $this->assertEquals(21, $model->related1_sum_number);
+    }
+
+    public function testLoadSumMultipleRelations()
+    {
+        $model = BaseModel::first();
+
+        DB::enableQueryLog();
+
+        $model->loadSum(['related1', 'related2'], 'number');
+
+        $this->assertCount(1, DB::getQueryLog());
+        $this->assertEquals(21, $model->related1_sum_number);
+        $this->assertEquals(12, $model->related2_sum_number);
+    }
+}
+
+class BaseModel extends Model
+{
+    public $timestamps = false;
+
+    protected $guarded = [];
+
+    public function related1()
+    {
+        return $this->hasMany(Related1::class);
+    }
+
+    public function related2()
+    {
+        return $this->hasMany(Related2::class);
+    }
+}
+
+class Related1 extends Model
+{
+    public $timestamps = false;
+
+    protected $fillable = ['base_model_id', 'number'];
+
+    public function parent()
+    {
+        return $this->belongsTo(BaseModel::class);
+    }
+}
+
+class Related2 extends Model
+{
+    public $timestamps = false;
+
+    protected $fillable = ['base_model_id', 'number'];
+
+    public function parent()
+    {
+        return $this->belongsTo(BaseModel::class);
+    }
+}