The M203 is made to be mounted underneath an M16 or an M4 type rifle.
Kourov uses an Egyptian AKM assault rifle with an M203 grenade launcher mounted underneath it. Rambo later takes this and a handful of 40mm grenades and uses it to destroy a truck of Soviet soldiers.Most soldiers use the AKM or even the older AK-47 in Rambo III. This is wrong. Most soldiers at the time were using the AK-74, chambered for the smaller 5.45x39mm cartridge. Why Kourov would even have an American M203 grenade launcher on his Egyptian weapon in the Soviet Army in the first place is unknown, espescially when you consider the fact that the two weapons were never designed to be used together (the M203 was designed for usage on M16s), and that you would have to grab the weapon by the magazine in order to efficiently fire it, which every experienced shooter knows not to do.
Reese carries an M4A1 carbine with an M203 mounted underneath it.