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The problem involves two people taking steps of 77 cm and 88 cm, respectively. We need to find the minimum distance (in cm) that both can cover in complete steps. This is a classic problem of finding the Least Common Multiple (LCM) of two numbers.

To find the minimum distance, we will calculate the LCM of 77 and 88.

### Steps:
1. Prime factorize both 77 and 88:
   - 77 = \( 7 \times 11 \)
   - 88 = \( 2^3 \times 11 \)

2. LCM is found by taking the highest powers of all prime factors:
   - LCM(77, 88) = \( 2^3 \times 7 \times 11 = 616 \)

Thus, the minimum distance both people can cover in complete steps is **616 cm**.

Would you like any further explanation or details on this process? Here are five related questions to think about:

1. How is the greatest common divisor (GCD) used in finding the LCM?
2. Can you solve the same problem using the GCD-LCM relationship formula?
3. What would happen if their step sizes were prime numbers?
4. How would the calculation change if more than two people were involved with different step sizes?
5. How can you determine the LCM of more complex numbers or larger primes?

**Tip:** LCM is particularly useful in problems involving synchronization of cycles, like when two events repeat at different intervals.

Two persons take steps of 77 cm and 88 cm, respectively. If they start in step, then what is the minimum distance (in cm) they should cover so that both of them can cover the distance in complete steps?

Learn how to find the least common multiple (LCM) of two step lengths, 77 cm and 88 cm, so that both persons can cover the same minimum distance in complete steps. This solution involves prime factorization and is suitable for students in Grades 6-8.

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