$$\frac{3}{7}\times\frac{4}{9}\times\frac{21}{5}\times\frac{5}{24}\times\frac{504}{1}$$
$84$
$$\frac{3\times 4}{7\times 9}\times \frac{21}{5}\times \frac{5}{24}\times \frac{504}{1}$$
$$\frac{12}{63}\times \frac{21}{5}\times \frac{5}{24}\times \frac{504}{1}$$
$$\frac{4}{21}\times \frac{21}{5}\times \frac{5}{24}\times \frac{504}{1}$$
$$\frac{4\times 21}{21\times 5}\times \frac{5}{24}\times \frac{504}{1}$$
$$\frac{4}{5}\times \frac{5}{24}\times \frac{504}{1}$$
$$\frac{4\times 5}{5\times 24}\times \frac{504}{1}$$
$$\frac{4}{24}\times \frac{504}{1}$$
$$\frac{1}{6}\times \frac{504}{1}$$
$$\frac{1}{6}\times 504$$
$$\frac{504}{6}$$
$$84$$
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$2^{2}\times 3\times 7$
