how many numbers between 200 and 600 are divisible by 4,5, and 6?

a smallest  positive number which is divisible by 4,5,6 is lcm of these numbers which is 60 ,

now if any number is multiple of 60 then the condition is satisfied ...

nearest to 200 , 240 is the first number  ....

now , a+(n-1)d = T_n

   a=240 , d = 60 , T_n = 600

     240+(n-1)60 = 600

     n= 7

that means there are 7 numbers......

240,300,360,420,480,540... are the numbers between 200 & 600 which is divisible by LCM (4,5,6), i.e 60.. so, there is 6 numbers between 200 & 600... answer is 6.