Q) If \(n\) is a natural number , then the largest natural number by which \(n(n + 1 )(n + 2 )\) is divisible, is
  • 1) 6
  • 2) 8
  • 3) 12
  • 4) 24


Answer : Option 4

Since , \(n\) is divisible by 2 , therefore \((n + 2 )\) is divisible by 4 , and hence \( n ( n + 2 )\) is divisible by 8
Also \( n , n + 1 , n + 2\) are three consecutive numbers and one of them is divisible by 3
hence , \( n(n + 1)(n + 2)\) must be divisible by 24

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