Find the least number which when divided by 6, 9, 14, 21 and 24 leaves 1, 4, 9, 16 and 19 as remainders respectively, but when divided by 17 leaves no remainder.  Choose the correct choice from the following choices:  A) 11277  B) 1003  C) 3277  D) 278  E) 181
LCM of 6, 9, 14, 21 and 24 is 504. Required number = (504 k–5) which is divisible by 17 for the least value of k. (504 k – 5) = (493k + 11k – 5) = (17×29)k + (11k–5) Let k = 1 ⇒ (11×1 – 5) = 7 (not divisible by 17) Let k ⇒ = 2 (11×2 – 5) = 17 (divisible by 17) ∴ (17×29)k + (11k–5) is exactly divisible by 17 for k = 2. ∴ Required Number   = (504)k – 5 = (504×2) – 5 = 1003.   Answer:1003
<result>B</result>
Find the least number which when divided by 6, 9, 14, 21 and 24 leaves 1, 4, 9, 16 and 19 as remainders respectively, but when divided by 17 leaves no remainder.