The previous answer is not only false, but can lead to very serious health implications. Co-administration of omeprazole/other PPIs/acid reducers/etc. along with thyroid meds (whether for TSH, T4, or others) can cause a drastic decrease in absorption of the thyroid medication. There are many peer reviewed studies that prove this, all one needs to do is a proper google search or a subscription to any of the popular medical journals.
Your stomach needs an acidic environment to properly convert your thyroid medication into a usable medication to get into your bloodstream, and if you take an acid reducer with your thyroid med this can cause problems.
IF YOU MUST take both (as I personally do because of my TSH levels reaching 24.6 plus ulcers and cancerous polyps due to GERD) make sure you take your acid reducing medication at least 4 hours BEFORE your thyroid medication (no matter what kind it is) and make sure not to take another acid reducing medication at least 4 hours AFTER your thyroid med.
If you do not separate the acid reducers 4 hours before and 4 hours after your thyroid medication your thyroid levels will become unstable and you will need to adjust your dosage. But in order to prevent your levels from getting out of whack and potentially causing more harm, just separate your meds as posted above and you should have no issue.
The above answer telling you that it is okay to take at the same time is incredibly harmful. Don't take my word for it (someone who has been dealing with both issues for a decade) trust the scientists that have figured this out through multiple peer reviewed studies.
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