Explanation:

Correct option 3: 78

Arithmetic mean of the numbers between 1 to 156 which are divisible by 2, 3, 4 and 6. 
Arithmetic Mean = Sum of observations / Total number of observations
Firstly, take LCM of 2, 3,4 and 6.
The LCM is 12. 
So, we have to find the sum of all the numbers which are divisible by 12 between 1 and 156.
The numbers which are divisible by 12 between 1 and 156 are as follows: Smallest number which is divisible by 12 between 1 and 156 is 12.
Largest number which is divisible by 12 between 1 and 156 is 144.
Sum= 12 +_ _ _ _ _  +144 = 12[1 + 2 + 3 + ---- 10 + 11 + 12]
Sum of n natural numbers= n(n+1)/2 where value of n is 12.
Sum=12[12(12 + 1)/2] = 12(12 x 13/2) = (12 x 12 x 13)/2 = 936
Arithmetic Mean = Sum of observations/Number of observations
Here, sum of observations = 936 Here, number of observations = 12
Arithmetic Mean = 936/12 = 78