Which of the following is divisible by the first five positive integer multiples of 23?
(i) 11110
(ii) 102120
(iii) 307740  Choose the correct choice from the following choices:
A) None  B) iii only  C) i and iii only  D) ii and iii only  E) i, ii and iii
A positive integer x is divisible by the first five integer multiples of 23 if and only if it is divisible by their least common multiple, 3*4*5*23=60*23= 
<gadget id="calculator">60*23</gadget>
<output>1_380</output>
1380.   The sum of the integers of 11110 is 4 so 11110 is not divisible by 3, hence not divisible by 1380.   102=17*6 and 120=20*6, so 102120=60*(1700+2)=60*1702=60*2*851. Now, 851-30*23=851-690= 
<gadget id="calculator">851-690</gadget>
<output>161</output>
161=7*23, so 102120 is divisibly by   60*23= 
<gadget id="calculator">  60*23</gadget>
<output>1_380</output>
1380.   Finally, 102120*3=306360, and   306360+1380= 
<gadget id="calculator">  306360+1380</gadget>
<output>307_740</output>
307740, so (iii) is also divisible by 1380.   Answer ii and iii only.
<result>D</result>
Which of the following is divisible by the first five positive integer multiples of 23?
(i) 11110
(ii) 102120
(iii) 307740