How many integers between 100 and 180, inclusive, cannot be evenly divided by 3 nor 5?	Select the correct option.
A) 39 B) 41 C) 43 D) 45 E) 47
The total numbers between 100 and 180, inclusive, is 81.   3*34= 
<gadget id="calculator">3*34</gadget>
<output>102</output>
102 and   3*60= 
<gadget id="calculator">  3*60</gadget>
<output>180</output>
180 so the number of multiples of 3 is 27.   5*20= 
<gadget id="calculator">5*20</gadget>
<output>100</output>
100 and   5*36= 
<gadget id="calculator">  5*36</gadget>
<output>180</output>
180 so the number of multiples of 5 is 17.   However, the multiples of 15 have been counted twice.   15*7= 
<gadget id="calculator">15*7</gadget>
<output>105</output>
105 and   15*12= 
<gadget id="calculator">  15*12</gadget>
<output>180</output>
180 so the number of multiples of 15 is 6.   Thus the total number is  81-27-17+6= 
<gadget id="calculator"> 81-27-17+6</gadget>
<output>43</output>
43.   The answer is 43.
<result>C</result>
How many integers between 100 and 180, inclusive, cannot be evenly divided by 3 nor 5?