Which is the least number that must be subtracted from 1256 so that the remainder when divided by 7, 12, 16 is 4?  Choices
A) 242 B) 232 C) 236 D) 240 E) 244
First we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}   LCM(7,12,16) = 48*7= 
<gadget id="calculator">48*7</gadget>
<output>336</output>
336   The numbers which will leave remainder 4 will be {336+4, 336x2 +4, 336x3 +4,...}   The largest such number less than or equal to 1256 is 336x3+4 or 1012   To obtain this you need to subtract 244.   244
<result>E</result>
Which is the least number that must be subtracted from 1256 so that the remainder when divided by 7, 12, 16 is 4?