How many positive integers less than 5,000 are evenly divisible by neither 15 nor 23?  Answers
A) 4,514	B) 4,475	C) 4,521	D) 4,428	E) 4,349
integers less than 5000 divisible by 15 5000/15 =333.something , so 333   integers less than 5000 divisible by 23 5000/23 = 238.## , so 238   we have double counted some, so take LCM of 15 and 23 =105 and divide by 5000, we get 47. so all numbers divisible by 15 and 23 = 333 +238 -47= 
<gadget id="calculator">333 +238 -47</gadget>
<output>524</output>
524   now subtract that from 4999. 4999- 524= 4521 answer 4,521.
<result>C</result>
How many positive integers less than 5,000 are evenly divisible by neither 15 nor 23?