Question:  Between the Battle of Pusan Perimeter and The Battle of Luzon which had the most combatants?

full_context: Document 1: Battle of Taegu: The Battle of Taegu was an engagement between UN and North Korean forces early in the Korean War, with fighting continuing from August 5–20, 1950 around the city of Taegu, South Korea. It was a part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously. The battle ended in a victory for the United Nations after their forces were able to drive off an offensive by North Korean divisions attempting to cross the Naktong River and assault the city.
Document 2: Battle of Bataan: The Battle of Bataan (7 January – 9 April 1942) represented the most intense phase of Imperial Japan's invasion of the Philippines during World War II. In January 1942, forces of the Imperial Japanese Army and Navy invaded Luzon along with several islands in the Philippine Archipelago after the bombing of the American naval base at Pearl Harbor. The commander-in-chief of all Filipino and American forces in the islands, General Douglas MacArthur, consolidated all of his Luzon-based units on the Bataan Peninsula to fight against the Japanese invaders. By this time, the Japanese controlled nearly all of Southeast Asia. The Bataan peninsula and the island of Corregidor were the only remaining Allied strongholds in the region. Despite a lack of supplies, Filipino and American forces managed to fight the Japanese for three months, engaging them initially in a fighting retreat southward. As the combined Filipino and American forces made a last stand, the delay cost the Japanese valuable time and prevented immediate victory across the Pacific. The surrender at Bataan, with 76,000 soldiers surrendering in the Philippines altogether, was the largest in American and Filipino military histories, and was the largest United States surrender since the American Civil War's Battle of Harper's Ferry. Soon afterwards, Filipino and American prisoners of war were forced into the Bataan Death March.
Document 3: Battle of the Visayas: The Battle of the Visayas was fought by U.S. forces and Filipino guerrillas against the Japanese from 18 March – 30 July 1945, in a series of actions officially designated as Operations Victor I and II, and part of the campaign for the liberation of the Philippines during World War II. The battle was waged to complete the recapture of the central portions south of the archipelago and secure them from remaining Japanese forces.
Document 4: Battle of Masan: The Battle of Masan was an engagement between United Nations (UN) and North Korean (NK) forces, which took place early in the Korean War between August 5 and September 19, 1950, in the vicinity of Masan and the Naktong River in South Korea. It was part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously. The battle ended in a victory for the UN after large numbers of United States (US) and Republic of Korea (ROK) troops were able to repel the repeated attacks of two North Korean divisions.
Document 5: Battle of Pusan Perimeter: The Battle of Pusan Perimeter was a large-scale battle between United Nations and North Korean forces lasting from August 4 to September 18, 1950. It was one of the first major engagements of the Korean War. An army of 140,000 UN troops, having been pushed to the brink of defeat, were rallied to make a final stand against the invading North Korean army, 98,000 men strong.
Document 6: Battle of Luzon: The Battle of Luzon, fought 9 January – 15 August 1945, was a land battle of the Pacific Theater of Operations of World War II by the Allied forces of the U.S., its colony the Philippines, and allies against forces of the Empire of Japan. The battle resulted in a U.S. and Filipino victory. The Allies had taken control of all strategically and economically important locations of Luzon by March 1945, although pockets of Japanese resistance held out in the mountains until the unconditional surrender of Japan. While not the highest in U.S. casualties, it is the highest net casualty battle U.S. forces fought in World War II, with 192,000 to 205,000 Japanese combatants dead (mostly from starvation and disease), 10,000 American combatants killed, and between 120,000 to 140,000 Filipino civilians and combatants killed.
Document 7: Battle of the Philippine Sea: The Battle of the Philippine Sea (June 19–20, 1944) was a major naval battle of World War II that eliminated the Imperial Japanese Navy's ability to conduct large-scale carrier actions. It took place during the United States' amphibious invasion of the Mariana Islands during the Pacific War. The battle was the last of five major "carrier-versus-carrier" engagements between American and Japanese naval forces, and pitted elements of the United States Navy's Fifth Fleet against ships and aircraft of the Imperial Japanese Navy's Mobile Fleet and nearby island garrisons. This was the largest carrier-to-carrier battle in history.
Document 8: Battle of the Bowling Alley: In the Battle of the Bowling Alley (August 12–25, 1950), United Nations (UN) forces defeated North Korean forces early in the Korean War near the city of Taegu, South Korea. The battle took place in a narrow valley, dubbed the "Bowling Alley", which was north of Taegu. It followed a week of fighting between the Korean People's Army (KPA) 13th Division and the Republic of Korea Army's (ROK) 1st Division along the latter's last defensible line in the hills north of the city. Reinforcements, including the US Army's 27th and 23rd Infantry Regiments were committed to bolster the South Koreans' defenses. This battle and several others were smaller engagements of the Battle of Pusan Perimeter.
Document 9: Battle of P'ohang-dong: The Battle of P'ohang-dong was an engagement between the United Nations and North Korean forces early in the Korean War, with fighting continuing from 5–20 August 1950 around the town of P'ohang-dong, South Korea. It was a part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously. The battle ended in a victory for the United Nations after their forces were able to drive off an attempted offensive by three North Korean divisions in the mountainous eastern coast of the country.
Document 10: Battle of Bataan (1945): The Battle for the Recapture of Bataan from 31 January to 21 February 1945, by US forces and Allied Filipino guerrillas from the Japanese, part of the campaign for the liberation of the Philippines, was waged to secure the western shore of Manila Bay to enable the use of its harbor and open new supply lines for American troops engaged in the crucial battle for the liberation of Manila.
Document 11: Battle of Ka-san: The Battle of Ka-san was an engagement between United Nations (UN) and North Korean forces early in the Korean War from September 1 to September 15, 1950, in the vicinity of Ka-san in South Korea. It was a part of the Battle of Pusan Perimeter, and was one of several large engagements fought simultaneously. The battle ended in a victory for the United Nations after large numbers of United States (US) and Republic of Korea (ROK) troops repelled a strong North Korean attack.
Document 12: Battle of Mindanao: The Battle of Mindanao was fought by United States forces and allied Filipino guerrillas against the Japanese from 10 March - 15 August 1945 on the island of Mindanao in the Philippines in a series of actions officially designated as Operation VICTOR V. It was part of the campaign to liberate the Philippines during World War II. The battle was waged to complete the recapture of the southernmost portions of the archipelago.
Document 13: Battle of Pusan Perimeter logistics: Logistics in the Battle of Pusan Perimeter (August 4 – September 15, 1950) during the Korean War played a decisive role in the battle. Efficient logistics, the management of personnel and materiel, supported United Nations (UN) supply lines while the North Koreans' routes of supply were steadily reduced and cut off. UN logistics improved throughout the Battle of Inchon and the defeat of the North Korean army at Pusan.
Document 14: Battle of Battle Mountain: The Battle of Battle Mountain was an engagement between United Nations (UN) and North Korean (NK) forces early in the Korean War from August 15 to September 19, 1950, on and around the Sobuk-san mountain area in South Korea. It was one of several large engagements fought simultaneously during the Battle of Pusan Perimeter. The battle ended in a victory for the UN after large numbers of United States (US) and Republic of Korea (ROK) troops were able to prevent a North Korean division from capturing the mountain area.
Document 15: Battle of Baguio (1945): The Battle of Baguio occurred between 21 February and 26 April 1945, and was part of the greater Luzon campaign during the Allied liberation of the Philippines at the end of World War II. During the battle, American and Philippine forces recaptured the city of Baguio on the island of Luzon from a Japanese occupation force. One of the last tank engagements of the Philippine campaign took place during the battle. Baguio later became the scene of the final surrender of Japanese forces in the Philippines in September 1945.
ground_truth: The Battle of Luzon