How many positive integers less than 5,000 are evenly divisible by neither 15 nor 22?  Choose the most appropriate option:	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 22 5000/22 = 238.## , so 238   we have double counted some, so take LCM of 15 and 22 =105 and divide by 5000, we get 47. so all numbers divisible by 15 and 22 = 333 +238 -47= 
<gadget id="calculator">333 +238 -47</gadget>
<output>524</output>
524   now subtract that from 4999. 4999- 524= 4514 answer 4,514.
<result>A</result>
How many positive integers less than 5,000 are evenly divisible by neither 15 nor 22?