I have submitted a solution for this problem 1349A - Orac and LCM and got AC wondering if this is really a property?
Submission: 321223203
i figured out that i can write:
GCD( lcm(a1,a2), lcm(a1,a3), lcm(a1,a4) ... lcm(a1,an)) = LCM(a1, GCD(a2,a3,a4,a5,...an))



