**Introduction:**
In this scenario, three persons are stepping off together during a morning walk. Each of them has a different step length, measuring 40cm, 42cm, and 45cm respectively. The objective is to determine the minimum distance each person should walk so that they all cover the same distance and complete an equal number of steps.

**Analysis:**
To find the minimum distance each person should walk, we need to consider the concept of finding the least common multiple (LCM) of the step lengths. The LCM is the smallest multiple that is divisible by all the given numbers.

**Method:**
To solve this problem, we will follow these steps:
1. Determine the prime factors of each step length.
2. Identify the highest powers of all prime factors.
3. Multiply the prime factors with the highest powers to obtain the LCM.
4. Divide the LCM by each individual's step length to find the number of steps each person should take.

**Step 1: Prime Factors**
Let's find the prime factors of each step length:
- 40cm = 2 * 2 * 2 * 5
- 42cm = 2 * 3 * 7
- 45cm = 3 * 3 * 5

**Step 2: Highest Powers**
Next, identify the highest powers of each prime factor:
- Prime factor 2: highest power = 3 (from 2 * 2 * 2)
- Prime factor 3: highest power = 2 (from 3 * 3)
- Prime factor 5: highest power = 1 (from 5)
- Prime factor 7: highest power = 1 (from 7)

**Step 3: LCM Calculation**
Now, multiply the prime factors with their highest powers to obtain the LCM:
- LCM = 2^3 * 3^2 * 5^1 * 7^1 = 8 * 9 * 5 * 7 = 2520cm

**Step 4: Number of Steps**
Finally, divide the LCM by each individual's step length to determine the number of steps each person should take:
- Person 1: 2520cm / 40cm = 63 steps
- Person 2: 2520cm / 42cm = 60 steps
- Person 3: 2520cm / 45cm = 56 steps

**Conclusion:**
In conclusion, to ensure that each person covers the same distance and completes an equal number of steps, Person 1 should walk a minimum distance of 2520cm (63 steps), Person 2 should walk 2520cm (60 steps), and Person 3 should walk 2520cm (56 steps). This will ensure that all three individuals cover the same distance and complete the same number of steps.