That's an interesting hypothesis you have! Unfortunately, it seems like you've made a multiplication mistake. 360100/2 = 18,000 but lcm(360, 100) = 1,800. They are off by a factor of 10. This property also doesn't hold true for all even numbers. Take 8 and 4 for instance. lcm(8, 4) = 8, but 84/2 = 16. However, you could ask yourself some follow up questions to keep exploring:
Why do 360100/2 and lcm(360, 100) differ by a factor of 10? What is special "how many 10s" are in a number (referring to the prime factorization of 10)? Challenge problem: how many zeroes does 98765432*1 end in?
What numbers does this property hold true for? If you have a and b, when does a*b/2 = lcm(a, b)?