6Step-by-step explanation:LET three consecutive positive integers be, n, n + 1 and n + 2.Whenever a number is divided by 3, the remainder obtained is either 0 or 1 or 2.∴ n = 3p or 3p + 1 or 3p + 2, where p is some integer.If n = 3p, then n is divisible by 3.If n = 3p + 1, then n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1) is divisible by 3.If n = 3p + 2, then n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3.So, we can SAY that ONE of the numbers among n, n + 1 and n + 2 is always divisible by 3.⇒ n (n + 1) (n + 2) is divisible by 3. SIMILARLY, whenever a number is divided 2, the remainder obtained is 0 or 1.∴ n = 2q or 2q + 1, where q is some integer.If n = 2q, then n and n + 2 = 2q + 2 = 2(q + 1) are divisible by 2.If n = 2q + 1, then n + 1 = 2q + 1 + 1 = 2q + 2 = 2 (q + 1) is divisible by 2.So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 2.⇒ n (n + 1) (n + 2) is divisible by 2. SINCE, n (n + 1) (n + 2) is divisible by 2 and 3. ∴ n (n + 1) (n + 2) is divisible by 6.