BEIJING, June 29 (Reuters) - Zinc shrugged off early losses to trade higher for a third day on Friday on the prospect of Chinese smelters cutting output by 10 percent in response to low prices and treatment charges. Helen Lau, an analyst at Argonaut Securities in Hong Kong, said a 10 percent cut implied that 400,000 tonnes of the metal would come out of the market in China, the world's biggest zinc producer, on an annualised basis. There is "a need for smelters to constrain their production because demand is weak especially the demand from galvanising," she added. Zinc is used to galvanise steel. The metal is on course to shed 11.3 percent in London and 5.2 percent in Shanghai in the second quarter, which would mark its worst quarter since the third quarter of 2015. LME zinc is also set for a drop of 6.3 percent in June alone, which would be its steepest monthly plunge since November 2015. FUNDAMENTALS * ZINC: Zinc on the London Metal Exchange was up 0.2 percent at $2,903.50 a tonne as of 0524 GMT, extending a 0.7 percent gain on Thursday. The most traded August zinc contract on the Shanghai Futures Exchange (ShFE) edged up 0.1 percent to 23,250 yuan $3,517.19) a tonne. * COPPER: Three-month copper on the LME rose 0.7 percent to $6,671.50 a tonne and is track for a 0.6 percent dip this quarter. ShFE copper fell by 0.2 percent but is still set for a 2.3 percent gain over the three months. * OTHER METALS: Shanghai nickel is set for its best quarter since the contract was launched in 2015, with a 18.5 percent rise, while lead is poised to add 16.2 percent this quarter amid an environmental crackdown in China. * TC/RCs: China's top copper smelters on Thursday failed to set minimum treatment and refining charges (TC/RCs) for copper concentrate in the third quarter of 2018, two people with knowledge of the matter said. * RUSAL: Shareholders at sanctions-hit Russian aluminium producer Rusal elected a new board of directors on Thursday in an effort to appease the U.S. and get the restrictions lifted.