Controlling 70+ LEDs with UNO R3

"I want to make a clock, so I'll need two independent circuits "
No, you just need a way to control 72 LEDs. Or 132, if you wanted a ring of seconds, a ring of minutes, a ring of hours.

Look at this circuit:
This controls 64 LEDs.
If you were to expand this to the right, and added 2 more of the chips along the bottom to control the additional columns, now you'd have 128 LEDs. Add another columns, and 2 more chips again, and you have 144.

Arrange 60 LEDs from the first 8 columns in a circle. 8 bytes of data will represent the status of those LEDs.
Arrange 60 LEDs from the 2nd 8 columns in a circle. 8 bytes of data will represent the status of those LEDs.
Arrange 12 LEDs from the last 2 columns in a circle. 2 bytes of data will represent the status of those LEDs.

Have some extra LEDs to represent AM & PM even.
Have some fun on minute changes & hour changes, run a fun pattern thru the circles or something.

To run it: have some fun mulitplexing - every mS or so read the byte of data for a column & send it and turn on the corresponding cathode.

The process was well discussed here
http://arduino.cc/forum/index.php/topic,114901.0.html

Simplify the design some - use a TPIC6B595 in place of the 74HC595/ULN2803s along the bottom.