\(\frac{3.5.7+6.10.14+9.15.21}{5.7.9+10.14.18+15.21.27}\)
= \(\frac{3.5.7+3.2.5.2.7.2+3.3.5.3.7.21}{5.7.9+5.2.7.2.9.2+5.3.7.3.9.3}\)
= \(\frac{3.5.7+3.5.7.2.2.2+3.5.7.3.3.3}{5.7.9+5.7.9.2.2.2+5.7.9.3.3.3}\)
= \(\frac{3.5.7+3.5.7.8+3.5.7.27}{5.7.9+5.7.9.8+5.7.9.27}\)
= \(\frac{3.5.7.\left(1+8+27\right)}{5.7.9.\left(1+8+27\right)}\)
= \(\frac{3.5.7.36}{5.7.9.36}\)
= \(\frac{1}{3}\)