The number of numbers lying between 1 and 200 which are divisible by either of 2 , 3 or 5? The number of numbers lying between 1 and 200 which are divisible by either of two , three or five?

A)numbers divisible by 2: $\frac{200}{2} = 100$
B)numbers divisible by 3: $\frac{200}{3} = 66$
C)numbers divisible by 5: $\frac{200}{5} = 40$
counting twice
AB)numbers divisible by 6: $\frac{200}{6} = 33$
AC)numbers divisible by 10: $\frac{200}{10} = 20$
BC)numbers divisible by 15: $\frac{200}{15} = 13$
counting 3 times 
ABC)numbers divisible by 30: $\frac{200}{30} = 6$
Total of numbers  = A + B + C - AB - AC - BC + ABC = 100 + 66 + 40 - 33 - 20 - 13 + 6 = 146
