Why It Could Pay to Sign Up for Social Security and Medicare at the Same Time
The decision to file for Social Security isn't an easy one. The age you claim benefits at will determine how much monthly income you collect throughout retirement, and it's therefore not a choice to take lightly.
You can first sign up for Social Security at age 62, and once you turn 70, you shouldn't hold off any longer because there's no financial incentive to do so. As such, 70 is usually considered the latest age to claim Social Security, even though you're not forced to sign up at that point.
Smack in the middle of that window are two other important milestones: age 65, when Medicare eligibility kicks in, and ages 66 to 67, which is when full retirement age (FRA) begins. FRA is when you're entitled to your full monthly Social Security benefit based on your earnings history. If you file before FRA, your monthly benefit will be reduced on a lifelong basis.
Source Fool.com