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

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