* LME/ShFE arb: http://bit.ly/2wZSAEz (Updates with closing prices)
LONDON, Dec 1 (Reuters) - Lead and zinc touched multi-week highs on Friday amid supply concerns as China steps up pollution inspections just as seasonal demand for lead in batteries increases.
Most other industrial metals also rose, supported by strong manufacturing data in much of Asia and Europe and a weaker dollar after reports that a former national security adviser to Donald Trump is prepared to testify against the U.S. President.
Production of lead and zinc, which are usually found in the same deposits, is expected to be hit in China by a crackdown on smog after authorities ordered the shutdown of polluting facilities.
"We're hearing that there are a lot more inspections, monitoring and maybe some temporary shutdowns, generally constraints on lead producers," said Robin Bhar, head of metals research at Societe Generale, adding that zinc would also be affected.
The peak demand period for lead, which is mainly used to make batteries, is the winter when freezing weather causes battery failures.
"Fundamentally, if you're looking for a seasonality play, lead would be number one, maybe getting a demand boost from a colder winter than people expected," Bhar added.
* LEAD: Benchmark lead on the London Metal Exchange rose 3 percent to $2,544 a tonne by the close, its highest since Nov. 10.
* LEAD SPREADS: Cash LME lead moved to a $2 premium over the benchmark three-month contract, indicating tightness of nearby supply, compared with a discount of $12.50 on Tuesday.
* ZINC: Three month LME zinc finished 3 percent higher at $3,249 a tonne after touching $3,269.50, its strongest since Nov. 1.
Zinc, mainly used for galvanised steel, was also supported by Shanghai steel futures, which traded near their highest level since mid-September.
* FACTORIES: The wider base metals complex received a boost from data showing that global manufacturing expanded at the fastest pace in years last month and the second-best in two decades in the euro zone, driven by robust demand.
* CAIXIN: While the Caixin/Markit survey of China's manufacturing activity grew at the weakest pace in five months in November, this is a survey largely focused on small and mid-sized companies. .
"For the Chinese PMI numbers to hold up as well as they have ... suggests that despite the (winter smog) closures, end-user Chinese demand is not being impacted all that much," said INTL FCStone analyst Edward Meir.
* COPPER: Three-month LME copper rose 1.1 percent to close at $6,833 a tonne after trading flat in the previous session.
* ALUMINIUM: LME aluminium climbed 1.3 percent to close at $2,074.50 a tonne.
* PREMIUMS: A global aluminium producer has offered Japanese buyers a premium of $110 a tonne for primary metal shipments during the first quarter of next year, as much as 17 percent above the current quarter, three sources directly involved in pricing talks said on Friday.
PRICES: LME nickel gained 1.6 percent to $11,290 a tonne while tin shed 0.7 percent to $19,455.
(Reporting by Eric Onstad; Editing by Mark Potter and David Goodman)