Missouri State Route 124 is an east-west highway in East-Central Howard County. It runs from Missouri State Route 240, near Fayette, to the Boone/Howard County line near Harrisburg. MO St Rt 124 does not pass through any towns in Howard County. MO St Rt 124 is multi-plexed in Howard County. Missouri Secondary State Route A, near Harrisburg. MO St Rt 124 intersects the following highways in Howard COunty. Missouri State Route 240, near Fayette.