This is more difficult then just abc.........

$abcdef$ = $\frac{6}{7} \times defabc$

$7 \times abcdef$ = $6 \times defabc$

$7 \times ( 10^{5}a+10^{4}b+10^{3}c+10^{2}d+10e+f$ ) = $6 \times (10^{5}d+10^{4}e+10^{3}f+10^{2}a+10b+c)$

$(7 \times 10^{5} - 6 \times 10^{2})a + (7 \times 10^{4} - 6 \times 10)b + (7 \times 10^{3} - 6)c$ = $(6 \times 10^{5} - 7 \times 10^{2})d + (6 \times 10^{4} - 7 \times 10)e + (6 \times 10^{3} - 7)f$

$10^{2} \times (7000-6)a + 10 \times (7000-6)b + (7000-6)c$ = $10^{2} \times (6000-7)d + 10 \times (6000-7)e + (6000-7)f$

$6994 \times ( 10^{2}a+ 10b +c )$ = $5993 \times (10^{2}d + 10e +f )$

$6994 \times (abc)$ = $5993 \times (def)$

$538(abc)$ = $461(def)$

As 538 and 461 don't have common factors

$abc=461$ $and$ $def=538$

$N= abcdef = 461538$