Question 289007
N - First integer
N+1 - Second consecutive integer
N+2 - Third consecutive integer
{{{N*(N+1)*(N+2)=21*(N+N+1+N+2)}}}

{{{N*(N+1)*(N+2)=21*(3N+3)}}}
{{{N*cross((N+1))*(N+2)=63*cross((N+1))}}}
{{{N*(N+2)=63}}}
{{{N^2+2N=63}}}
{{{N^2+2N-63=0}}}
{{{ (N-7)(N+9)=0 }}}
Two solutions:
{{{ N-7=0}}}
{{{ N=7}}}
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.
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{{{ N+9=0}}}
{{{ N=-9
}}}
The problem only asks for "three consecutive positive integers" so N=-9 is not a solution.
The three integers are 7,8, and 9.