If \frac{421}{972} = \frac{1}{a + \frac{1}{b+ \frac{1}{c+ \frac{1}{d+ \frac{1}{e}}}}} then what is the value of a\times b\times c\times d\times e?

Explanation

We write 972/421 as a continued fraction: 972 = 2 \times 421 + 130 \implies a=2. Next, 421 = 3 \times 130 + 31 \implies b=3. Then, 130 = 4 \times 31 + 6 \implies c=4. Finally, 31 = 5 \times 6 + 1 \implies d=5 and e=6. The product is 2 \times 3 \times 4 \times 5 \times 6 = 720.

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