Pokemon Red, Blue, and Yellow HM and TM Locations
Locations of all 5 Hidden Machines (HMs) and 50 Technical Machines (TMs) in the Kanto region in Pokemon Red, Blue, and Yellow Versions on Gameboy and 3DS Virtual Console. Contains Story Spoilers. Information pulled from multiple sources including Serebii.net

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Hidden Machines
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HM01 Cut - SS Anne Upper Deck, given by the Captain
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HM02 Fly - Route 16, given by a girl in the house in the northwest area of the route (requires Cut)
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HM03 Surf - Safari Zone Area 3, from a man in the Secret House
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HM04 Strength - Fuchsia City, given by the Safari Zone Warden after returning his Gold Teeth
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HM05 Flash - Route 2, given by Professor Oak's aide in the gate as a reward for registering 10 Pokemon in the Pokedex (requires Cut)
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Technical Machines
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TM01 Mega Punch - Mt. Moon B2F, on a plateau far east of a Team Rocket Grunt in a closed-off room accessible from the ladder between the two other ladders on 1F; Celadon Department Store (₽3000)
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TM02 Razor Wind - Rocket Hideout B4F, in the northwest area of the floor; Celadon Department Store (₽2000)
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TM03 Swords Dance - Silph Co. 7F, in the eastern room
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TM04 Whirlwind - Route 4, on the second-highest plateau in the north area of the route
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TM05 Mega Kick - Victory Road 2F, southeast of the Black Belt, Celadon Department Store (₽3000)
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TM06 Toxic - Given by Koga after defeating the Fuchsia City gym
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TM07 Horn Drill - Rocket Hideout B2F, southeast of the Moon Stone located in the northwest of the spin tile maze; Celadon Department Store (₽2000)
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TM08 Body Slam - SS Anne 1F, 2nd room from left
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TM09 Take Down - Silph Co. 5F in the southwest area of the floor; Celadon Department Store (₽3000)
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TM10 Double-Edge - Rocket Hideout B3F, south of the staircase leading to B2F
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TM11 Bubble Beam - Given by Misty after defeating the Cerulean City gym
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TM12 Water Gun - Mt. Moon 1F, near the southwest corner of the floor
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TM13 Ice Beam - Celadon Department Store Roof, given by a girl in exchange for a Fresh Water
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TM14 Blizzard - Pokemon Mansion B1F, east of the southernmost statue
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TM15 Hyper Beam - Celadon Game Corner (5500 Coins)
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TM16 Pay Day - Route 12, on an island southeast of the Lavender City gate (requires Surf)
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TM17 Submission - Victory Road 2F in the northeast area of the floor; Celadon Department Store (₽3000)
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TM18 Counter - Celadon Department Store 3F, given free from a clerk
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TM19 Seismic Toss - Northwest of the cuttable tree (requires defeating a trainer or Cut)
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TM20 Rage - Route 15, in the northwest area of the route (requires Cut)
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TM21 Mega Drain - Given by Erika after defeating the Celadon City gym
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TM22 Solar Beam - Pokemon Mansion B1F, in the northwest area of the floor
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TM23 Dragon Rage - Celadon Game Corner (3300 Coins)
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TM24 Thunderbolt - Given by Lt. Surge after defeating the Vermilion City gym
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TM25 Thunder - Power Plant, in the southeast area of the facility
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TM26 Earthquake - Silph Co. 10F, in the southwest room
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TM27 Fissure - Given by Giovanni after defeating the Viridian City gym
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TM28 Dig - Given by a Team Rocket Grunt in Cerulean City after defeating him in the burglarized house
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TM29 Psychic - Saffron City, given by Mr. Psychic in his house on the southeastern side of the city
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TM30 Teleport - Route 9, in the southwest corner of the route
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TM31 Mimic - Saffron City, given by the Copycat girl after giving her a Poke Doll
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TM32 Double Team - Safari Zone Area 3, southeast of the Secret House; Celadon Department Store (₽1000)
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TM33 Reflect - Power Plant, in the area east of the south entrance, northwest of a Voltorb; Celadon Department Store (₽1000)
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TM34 Bide - Given by Brock after defeating the Pewter City gym
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TM35 Metronome - Cinnabar Island Pokemon Research Lab, given by a scientist
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TM36 Self-Destruct - Silph Co. 2F, given by a woman in the northwest room
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TM37 Egg Bomb - Safari Zone Center Area East, in the patch of grass beside the water; Celadon Department Store (₽2000)
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TM38 Fire Blast - Given by Blaine after defeating the Cinnabar Island gym
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TM39 Swift - Route 12, given by the girl on the second floor of the Lavender guardhouse
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TM40 Skull Bash - Safari Zone Area 2, southwest of the rest house
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TM41 Soft-Boiled - Celadon City, given by a man north of the pond (requires Surf)
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TM42 Dream Eater - Viridian City, given by a man sleeping in the southwestern part of the city (requires Cut or Surf)
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TM43 Sky Attack - Victory Road 1F, in the north area of the floor (may need to "reset" the Strength boulder)
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TM44 Rest - SS Anne B1F, in the fourth room from the right
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TM45 Thunder Wave - Route 24, on the east side of a plateau in the northwest area of the route
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TM46 Psywave - Given by Sabrina after defeating the Saffron City gym
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TM47 Explosion - Victory Road 3F, in the northwest area of the floor
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TM48 Rock Slide - Celadon Department Store Roof, given by a girl in exchange for a Soda Pop
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TM49 Tri Attack - Celadon Department Store Roof, given by a girl in exchange for a Lemonade
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TM50 Substitute - Celadon Game Corner (7700 Coins)