Remainders LCM HCF

Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12, and 16 is 4.

  1. 137
  2. 140
  3. 172
  4. 1361

Answer

LCM (7,12,16) = 48*7 = 336

The numbers which will leave remainder 4 will be {336+4, 336*2 +4, 336*3 +4,...}

The largest such number less than or equal to 1856 is 336*5+4 or 1684

To obtain this you need to subtract 172 from 1856.

The correct option is C.