A person has three iron rods of length 10, 15 & 20 m respectively. He wants to divide all three of them in smaller pieces of equal lengths. How many minimum pieces can he cut from them without wasting any material?

Options

A. 45
B. 15
C. 9
D. 30

Answer

To solve the problem of dividing three iron rods of lengths 10 m, 15 m, and 20 m into smaller pieces of equal lengths without wasting any material, we need to follow these steps:

### Step 1: Find the HCF (Highest Common Factor)
To determine the maximum length of the smaller pieces that can be cut from all three rods without any wastage, we need to find the HCF of the lengths of the rods.

- The lengths of the rods are: 10 m, 15 m, and 20 m.
- We can find the HCF by factorizing each length:
- 10 = 2 × 5
- 15 = 3 × 5
- 20 = 4 × 5

The common factor among these lengths is 5. Therefore, the HCF of 10, 15, and 20 is **5 m**.

### Step 2: Calculate the Number of Pieces for Each Rod
Next, we will calculate how many pieces of 5 m can be cut from each rod.

1. For the 10 m rod:
\[ \text{Number of pieces} = \frac{10}{5} = 2 \text{ pieces} \]

2. For the 15 m rod:
\[ \text{Number of pieces} = \frac{15}{5} = 3 \text{ pieces} \]

3. For the 20 m rod:
\[ \text{Number of pieces} = \frac{20}{5} = 4 \text{ pieces} \]

### Step 3: Calculate the Total Number of Pieces
Now, we add the number of pieces obtained from each rod to find the total number of pieces.

\[ \text{Total pieces} = 2 + 3 + 4 = 9 \text{ pieces} \]

### Final Answer
The minimum number of pieces that can be cut from the three rods without wasting any material is **9 pieces**.

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