How did establishing the Medicare program reflect the ideas of the Great Society programs?

In the United States, Medicare is a single-payer, national social insurance program administered by the US federal government since 1966, currently using about 30-50 private insurance companies across the United States under contract for administration. [1] United States Medicare is funded by a payroll tax, premiums and surtaxes from beneficiaries, and general revenue. It provides health insurance for Americans aged 65 and older who have worked and paid into the system through the payroll tax. It also provides health insurance to younger people with some disabilities status as determined by the Social Security Administration, as well as younger people with end stage renal disease and amyotrophic lateral sclerosis.