Answer:
The only number he could choose is 90 
Step-by-step explanation:
Simply put, we want to find the numbers between 67 and 113 which are multiples of 3,5 and 6.
Kindly note that, the numbers we will be choosing will be multiples of the three numbers at the same time.
Multiples of 3 here are;
72 , 75 , 78 , 81 , 84 , 87 , 90 , 93 , 96 , 99 , 102 , 105 , 108 , 111
Multiples of 6 here are
72, 78 , 84 , 90 , 96 , 102 , 108 
Multiples of 5 here are 
70, 75 , 80 , 85 , 90 , 95 , 100 , 105 , 110
So therefore, the only number that works here is the number 90