May 16 (Reuters) - Prices of non-ferrous metals climbed on Thursday, backed by a softer dollar after U.S. inflation showed signs of slowing, making greenback-priced commodities cheaper for holders of other currencies.

Three-month copper on the London Metal Exchange (LME) was up 1.6% at $10,381.50 per metric ton, as of 0436 GMT, while the most-traded June copper contract on the Shanghai Futures Exchange (SHFE) advanced 1.1% to 82,520 yuan ($11,435.54) a ton.

The dollar skidded to multi-month lows after U.S. core inflation hit its slowest in three years, pulling forward expectations for rate cuts in the world's biggest economy and drawing bets that the U.S. currency may have peaked, for now.

Prices of base metals were lifted by inflows of funds betting on supply disruptions and an increasing need to use the metals in the green energy sectors, as well as on hopes of rate cuts that could further pressure the dollar and boost economic growth and metals demand in general.

Still, higher copper prices - up by around a fifth so far this year - have hurt physical demand. Importers in top consumer China now get a discount of $2 a ton to take copper in, compared with a premium of more than $100 a ton last December.

LME aluminium increased 1% to $2,623.50 a ton, nickel rose 0.7% to $19,630, zinc climbed 0.9% to $3,004, lead was up 0.6% at $2,283.50 and tin jumped 2.1% to $34,100.

SHFE aluminium climbed 2.1% to 20,885 yuan a ton, nickel increased 1.9% to 146,860 yuan, zinc was up 0.6% at 23,870 yuan, lead rose 1.4% to 18,890 yuan and tin advanced 1% to 276,600 yuan.

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($1 = 7.2161 yuan) (Reporting by Mai Nguyen in Hanoi; Editing by Sherry Jacob-Phillips)