show that the product of any three consecutive positive integers is divisible by 6
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Let, the integers be x, x+1 and x+2 respectively.
Adding
x+x+1+x+2
=3x+3
=3(x+1)
Which shows that the product is a multiple of 3
Therefore, it will be a multiple of 6 too which shows it is divisible by 6.
Adding
x+x+1+x+2
=3x+3
=3(x+1)
Which shows that the product is a multiple of 3
Therefore, it will be a multiple of 6 too which shows it is divisible by 6.
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