SOLUTION: The sum of the digits in the smallest positive integer that is divisible by 2, 4, 6, 10, 12, and 14 is: (A) 3 (B) 6 (C) 9 (D) 15 (E) 18

Algebra ->  Divisibility and Prime Numbers  -> Lessons -> SOLUTION: The sum of the digits in the smallest positive integer that is divisible by 2, 4, 6, 10, 12, and 14 is: (A) 3 (B) 6 (C) 9 (D) 15 (E) 18      Log On


   

Question 277966: The sum of the digits in the smallest positive integer that is divisible by 2, 4, 6, 10, 12, and 14 is:
(A) 3 (B) 6 (C) 9 (D) 15 (E) 18
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

  2 = 2
  4 = 2 x 2
  6 = 2     x 3
 10 = 2         x 5
 12 = 2 x 2 x 3
 14 = 2             x 7
LCM = 2 x 2 x 3 x 5 x 7 = 420

The smallest such number is their LCM, or 420

So the sum of the digits is 4 + 2 + 0 = 6, choice (B)

Edwin