Two pencils are the 24 cm and 42 cm . If we want to make them of equal size then minimum no. of similar pencils is :

Options

A. 6
B. 11
C. 12
D. None of these

Answer

To solve the problem of making two pencils of lengths 24 cm and 42 cm into equal sizes with the minimum number of similar pencils, we can follow these steps:

### Step 1: Find the Greatest Common Divisor (GCD)
To find the minimum size of the similar pencils, we first need to determine the greatest common divisor (GCD) of the two lengths (24 cm and 42 cm).

- **Calculation of GCD:**
- The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
- The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
- The common factors are: 1, 2, 3, 6
- The greatest common factor is 6.

### Step 2: Divide Each Length by the GCD
Next, we divide each pencil length by the GCD to find out how many similar pencils of that size can be made.

- **For the 24 cm pencil:**
\[ \text{Number of similar pencils} = \frac{24}{6} = 4 \]

- **For the 42 cm pencil:**
\[ \text{Number of similar pencils} = \frac{42}{6} = 7 \]

### Step 3: Calculate the Total Number of Similar Pencils
Now, we add the number of similar pencils from both lengths to find the total number of similar pencils needed.

\[ \text{Total similar pencils} = 4 + 7 = 11 \]

### Final Answer
Thus, the minimum number of similar pencils of equal size is **11**.

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