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Note that this is a Europe focused lesson. Your active focus is Latin America.
Learn about a lo mejor/igual/lo mismo in Spanish
The adverbs: a lo mejor, igual and lo mismo, can all be translated as "maybe" are always used with the Modo indicativo, even though they are expressing doubt. These are used very often and more colloquially than quizá/quizás/tal vez. See Using the subjunctive or the indicative after tal vez and quizás to express doubt in Spanish to learn about these.
Here are some examples:
A lo mejor vamos a Mallorca este verano.We may go to Mallorca this summer.
Juan no ha llegado todavía. Igual se ha quedado dormido.Juan hasn't arrived yet. Maybe he overslept.
Pedro y Carmen se miran mucho y se sonrojan. Lo mismo se gustan.Pedro and Carmen look at each other a lot and blush. Maybe they like each other.
A lo mejor, igual and lo mismo are all interchangeable and equally colloquial.
Bear in mind these are invariable - they act as adverbs and they don't need to agree with any other element in the sentence.
Here are some other examples:
Igual me apunto a esas clases de francés.I may sign up for those French lessons.
Lo mismo coincidimos con Miguel y Carlos en el concierto. Dijeron que a lo mejor iban.We may meet Miguel and Carlos at the concert. They said they might go.
No sé cómo lo saben mis padres. Igual mi hermano se chivó.I don't know how my parents know. Maybe my brother snitched on me.
Estoy muy estresada. A lo mejor pido un día libre en el trabajo.I'm very stressed. Maybe I'll ask for a day off work.
A lo mejor me compro ese vestido que vi ayer.I may buy that dress I saw yesterday.
Nadie responde..., lo mismo el restaurante ha cerrado.Nobody is answering..., maybe the restaurant closed down.
See also Using definite articles + mismo to say "the same" in Spanish
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