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British English would usually use "-our" and "-ser" and American English would use "-or" and "-zer".

I don't seem to find an appropriate answer to this. Which combination is actually correct for British and for American English.

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I'm not sure why you couldn't find the answer in a dictionary.

For British English it can (like most use-/ize words) be either:

deodorize

(dioʊdəraɪz ) Word forms: 3rd person singular present tense deodorizes , present participle deodorizing , past tense, past participle deodorized

REGIONAL NOTE:
in BRIT, also use deodorise

Collins Dictionary

In US English, it is deodorize:

deodorize verb

de·​odor·​ize | \ dē-ˈō-də-ˌrīz \

deodorized; deodorizing; deodorizes

Merriam-Webster

And it is never spelt with ou.

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In British English it's normally spelt either "deodorant" or "air freshener" depending on whether you want to deodorise a person or a room.

Apparently, according to Collins, "deodorizer" and "deodoriser" are both acceptable in British English, but I can't say I've ever heard of them in 30-something years of living in South East England.

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