n and even natural number then the largest natural number by which n(n+1)(n+2) is divisible, is
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n,
n + 1 and n + 2 are three consecutive positive integers.
When n = 2,
n (n + 1) (n + 2) = 2 (2 + 1)(2 + 2) = 2 × 3 × 4 = 24.
Thus, n (n + 1) (n + 2) is divisible by 24.
Note: The product of three consecutive natural numbers, n (n + 1) (n + 2) is divisible by 6.
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