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As I recall, it took about a month or so. I was also taking a low dose of B-complex. 1000 mcg of a sublingual lozenge of B12 is a good average amount to try. Many people find that after 6 months of this, they are able to reduce their thyroid meds.
When the proper amount of B's are supplied, they can help balance electrolytes, which in turn may help with blood pressure. It may also help lower BP to increase potassium in diet. This should be done very carefully if the BP med. is a potassium sparing type, though.