Question

Which of the following is the minimum length of a rope which can be cut into pieces of length 7 cm or 9 cm or 10 cm?

• A. 63 cm
• B. 810 cm
• C. 490 cm
• D. 630 cm

Answer 1

The correct option is D 630 cm

Given that the rope has to be cut into pieces of length $7\text{cm}$ or $9\text{cm}$ or $10\text{cm}$, the length of rope must be divisible by $7,9$ and $10$.

$7,9$ and $10$ are relatively prime numbers so the least number divisible by $7,9$ and $10$ is $7\times 9\times 10=630$.

$\therefore$ Minimum length of rope that can be cut into pieces of length $7,9$ and $10$ cm is $630$.