$1 \frac{1}{5} \times 1 \frac{1}{6} \times 1 \frac{2}{7}=$

Step 1 ：\(1 \frac{1}{5} = \frac{6}{5}\)

Step 2 ：\(1 \frac{1}{6} = \frac{7}{6}\)

Step 3 ：\(1 \frac{2}{7} = \frac{9}{7}\)

Step 4 ：\(\frac{6}{5} \times \frac{7}{6} \times \frac{9}{7} = \frac{378}{210}\)

Step 5 ：\(\frac{378}{210} = \frac{9}{5}\)

Step 6 ：\(\boxed{1 \frac{4}{5}}\)