How many positive integers less than 5,000 are evenly divisible by neither 13 nor 21?  Choices:
A) 4,514  B) 4,475  C) 4,521  D) 4,428  E) 4,349
integers less than 5000 divisible by 13 5000/13 =333.something , so 333   integers less than 5000 divisible by 21 5000/21 = 238.## , so 238   we have double counted some, so take LCM of 13 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 13 and 21 = 333 +238 -47= 
<gadget id="calculator">333 +238 -47</gadget>
<output>524</output>
524   now subtract that from 4999. 4999- 524= 4349 answer 4,349.
<result>E</result>
How many positive integers less than 5,000 are evenly divisible by neither 13 nor 21?