Our Pokemon Let's Go Pikachu and Let's Go Eevee Legendaries guide gives you all the information and strategy tips you need to capture all Legendary Pokemon in the Kanto region.

Articuno is one of the three Legendary Birds that can be caught in the same way in either version of the game. After defeating the leader of Fuchsia City Gym, you'll be able to surf south of the city and find Seafoam Islands. At the bottom of this cave you'll find Articuno.
To catch Articuno, you'll first need to defeat it in a timed 5 minute battle. Afterwards, you'll have the chance to catch it just like any other Pokemon in the game. Simply toss Ultra Balls at it until you've caught it, Articuno won't run away.
Articuno also has a very small chance to spawn in the sky. Once you've defeated the Elite Four, you'll be able to fly in the sky and can encounter this rare spawn. If you failed to catch Articuno on your first encounter, you can return here after defeating the Elite Four to try again.

Zapdos is the second of the three Legendary Birds that can be caught in the same way in either version of the game. After getting Sea Skim in Fuchsia City, you'll be able to surf east of Cerulean City to the Power Plant. If you navigate through the Power Plant to the end you'll find Zapdos.
To catch Zapdos, you'll first need to defeat it in a timed 5 minute battle. Afterwards, you'll have the chance to catch it just like any other Pokemon in the game. Simply toss Ultra Balls at it until you've caught it, Zapdos won't run away.
Zapdos also has a very small chance to spawn in the sky. Once you've defeated the Elite Four, you'll be able to fly in the sky and can encounter this rare spawn. If you failed to catch Zapdos on your first encounter, you can return here after defeating the Elite Four to try again.

Moltres is the final of the three Legendary Birds that can be caught in the same way in either version of the game. After defeating the eighth gym leader in Viridian City, you'll be able to take Victory Road to the Elite Four. On the bottom floor of the Victory Road caverns, you'll find Moltres.
To catch Moltres, you'll first need to defeat it in a timed 5 minute battle. Afterward, you'll have the chance to catch it just like any other Pokemon in the game. Simply toss Ultra Balls at it until you've caught it, Moltres won't run away.
Moltres also has a very small chance to spawn in the sky. Once you've defeated the Elite Four, you'll be able to fly in the sky and can encounter this rare spawn. If you failed to catch Moltres on your first encounter, you can return here after defeating the Elite Four to try again.

Mewtwo is the only Pokemon that can only be obtained once per game (except by trading) in Let's Go Pikachu or Let's Go Eevee. To catch Mewtwo, you'll need to navigate through Cerulean Cave near Cerulean City. The cave can only be accessed after the Elite Four has been defeated.
Unlike the Legendary birds, Mewtwo can be rather difficult to catch. This makes him a good candidate for the Master Ball. However, he won't run away, so you can keep tossing balls at him until he's caught as long as you have them.

Like many previous Pokemon games, there is no way to catch Mew in game. The only way to obtain Mew is to transfer one from a Pokeball Plus ($50) purchased near the launch of the games, or trade with someone who did. If you've done this, complete the following steps to get Mew:
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