The product of any three consecutive positive | vedclass

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Question

(A) Let the three consecutive positive integers be $n, (n+1)$,and $(n+2)$.The product of these integers is $P = n(n+1)(n+2)$.This expression represent

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(A) Let the three consecutive positive integers be $n, (n+1)$,and $(n+2)$.The product of these integers is $P = n(n+1)(n+2)$.This expression represents the product of three consecutive integers.We know that in any set of $k$ consecutive integers,there is always at least one multiple of $k!$ (k factorial).For $k=3$,the product is always divisible by $3! = 3 	imes 2 	imes 1 = 6$.For example,if $n=1$,$1 	imes 2 	imes 3 = 6$ (divisible by $6$).If $n=2$,$2 	imes 3 	imes 4 = 24$ (divisible by $6$).If $n=3$,$3 	imes 4 	imes 5 = 60$ (divisible by $6$).Thus,the product of any three consecutive positive integers is always divisible by $6$.

The product of any three consecutive positive integers is always divisible by . . . . . . .

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