The least common multiple of 1!+2!+3!, 2!+3!+4!, and 3!+4!+5! can be expressed in the form a*b!, where a and b are integers and b is as large as possible. What is a+b?

LCM{1!+2!+3!, 2!+3!+4!, 3!+4!+5!} ==LCM{9, 32, 150} ==7,200

7,200 ==10 * 6!

10 + 6 ==16