How many positive integers less than 80 are multiples of 4 but NOT multiples of 6? Select the correct option.
A) 4
B) 6
C) 8
D) 10
E) 12
The LCM of 4 and 6 is 12.   If x &lt;80 and x is divisible by 4 not by 6 --&gt; x is NOT divisible by 12.   From 1--&gt; 80, we have 6 numbers which is divisible by 12: 12, 24, 36, 48, 60, 72.   From 1--&gt;80, we have (72-4)/4 +1= 
<gadget id="calculator">(72-4)/4 +1</gadget>
<output>18</output>
18 numbers divisible by 4.   Therefore, our answer is 18-6= 
<gadget id="calculator">18-6</gadget>
<output>12</output>
12 numbers.   12
<result>E</result>
How many positive integers less than 80 are multiples of 4 but NOT multiples of 6?