Is the word multinacional the same in Brazilian and European Portuguese?

Yes

The word "multinacional" is identical in spelling, meaning, and grammatical function in both Brazilian and Continental Portuguese. The only differences are phonetic. In Brazilian Portuguese, the final "l" is typically vocalized, sounding like a "u" (mu-lti-na-cio-NAU), and unstressed vowels tend to be more open. In Continental Portuguese, the final "l" is more alveolar (the tongue touches the teeth), and unstressed vowels are often more closed or even reduced.

Brazilian Portuguese Examples:

1. Eu trabalho em uma multinacional de tecnologia. (I work in a multinational technology company.)
2. Essa multinacional abriu uma nova fábrica no Brasil. (This multinational opened a new factory in Brazil.)
3. Ele tem muita experiência em empresas multinacionais. (He has a lot of experience in multinational companies.)
4. A multinacional anunciou cortes de custos. (The multinational announced cost cuts.)
5. É difícil competir com uma multinacional tão grande. (It is difficult to compete with such a large multinational.)

Continental Portuguese Examples:

1. Eu trabalho numa multinacional de informática. (I work in a multinational IT company.)
2. Esta multinacional instalou-se cá há pouco tempo. (This multinational set up here not long ago.)
3. Ele tem vasta experiência em multinacionais. (He has vast experience in multinationals.)
4. A multinacional reduziu o número de funcionários. (The multinational reduced the number of employees.)
5. É difícil competir com uma multinacional desta dimensão. (It is difficult to compete with a multinational of this size.)