I don't need to pay for power to my computer. Is it a good idea to mine LTC or BTC on Intel Core Duo processor?
My CPU is 2 x 2.6GHz (computer woks 24/7)
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Mining on both Bitcoin and Litecoin is now dominated by ASICs. Even with Litecoin, you'd only mine at best about US$0.45 worth in a year.
You should have better luck if you can find a cryptocoin based on something besides SHA-256 or scrypt, for which there is no GPU or ASIC mining, such as Riecoin or Darkcoin. http://cpucoinlist.com/ lists some more CPU-friendly coins.
Both of these links discuss how to CPU mine profitably.
But if you don't pay for power... Try to partner up with someone with a good mining rig and divide the profits.