If you're getting disability income from Social Security you’re eligible for Medicare Part A (Hospital Insurance) and Part B (Medical Insurance) starting the 25th month you get the benefits.
Use this to determine your eligibility:
https://www.medicare.gov/eligibilitypremiumcalc/
Most LTD reduces benefits by the amounts you can get by the amount of SSDI and Medicare you are eligible for (so essentially, you have to apply when eligible to continue coverage).
Here is an article that simplifies it a bit:
Medicare Disability Coverage For Those Under 65
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