The LCM of two multiples of12 is 1056 . If one of the numbers is 132 then other number is

Options

A. 12
B. 72
C. 96
D. 132

Answer

To find the other number when one of the multiples of 12 is given as 132 and their LCM is 1056, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- LCM of the two numbers = 1056
- One number (multiple of 12) = 132

2. **Understand the Relationship**:
- The two numbers can be represented as multiples of 12. Let the other number be represented as \( 12y \) (where \( y \) is an integer).

3. **Use the Relationship Between LCM and HCF**:
- The formula relating the two numbers, their LCM, and HCF is:
\[ \text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} \]
- Here, \( a = 132 \) and \( b = 12y \). The HCF of both numbers is 12 (since both are multiples of 12).

4. **Substitute the Known Values into the Formula**:
- The formula becomes:
\[ 1056 = \frac{132 \times (12y)}{12} \]
- Simplifying this gives:
\[ 1056 = 11 \times 12y \]

5. **Solve for \( y \)**:
- Rearranging the equation:
\[ 12y = \frac{1056 \times 12}{132} \]
- Simplifying further:
\[ 12y = 1056 \div 11 \]
- Calculate \( 1056 \div 11 \):
\[ 12y = 96 \]
- Now, divide both sides by 12:
\[ y = \frac{96}{12} = 8 \]

6. **Find the Other Number**:
- The other number is:
\[ 12y = 12 \times 8 = 96 \]

### Final Answer:
The other number is **96**.