TOKYO - Factories in Asia's largest economies stepped up a gear in May as supply chain problems eased, business surveys showed on Thursday, but sluggish global demand remained a major challenge for many of the region's big exporters. Purchasing managers' indexes (PMIs) for China and Japan showed swings in factory activity to growth in the month, in contrast to weak indicators from South Korea, Vietnam and Taiwan where declines continued. The patchy set of PMIs pointed to an uneven recovery from the pandemic, particularly in China, the world's second-largest economy, and clouds the outlook for growth in the region, but still provided some cause for optimism. "The PMI surveys sugg...Keep on reading: Asia’s factories struggle for momentum amid patchy recovery