Three boys step off together from the same place. If their steps measure 36 cm. 48 cm and 54 cm at what distance from the starting point will they again step together ?

Answer

To find the distance at which the three boys will step together again, we need to calculate the Least Common Multiple (LCM) of their step measurements: 36 cm, 48 cm, and 54 cm. Here’s how to do it step by step:

### Step 1: Prime Factorization
First, we will find the prime factorization of each of the step measurements.

- **36**:
- 36 = 2 × 18
- 18 = 2 × 9
- 9 = 3 × 3
- So, 36 = 2² × 3²

- **48**:
- 48 = 2 × 24
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- So, 48 = 2⁴ × 3¹

- **54**:
- 54 = 2 × 27
- 27 = 3 × 9
- 9 = 3 × 3
- So, 54 = 2¹ × 3³

### Step 2: Identify the Highest Powers of Each Prime Factor
Next, we identify the highest power of each prime factor from the factorizations:

- For **2**: The highest power is 2⁴ (from 48).
- For **3**: The highest power is 3³ (from 54).

### Step 3: Calculate the LCM
Now, we can calculate the LCM by multiplying these highest powers together:

LCM = 2⁴ × 3³
= 16 × 27
= 432

### Conclusion
Thus, the distance from the starting point at which all three boys will step together again is **432 cm**.

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