The LCM of two multiples of 12 is 1056. If one of the number is 132, the other number is

Options

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

Answer

To find the other number when the LCM of two multiples of 12 is given, we can follow these steps:

### Step 1: Understand the relationship between LCM, GCD (or SCF), and the numbers.
We know that for any two numbers \( A \) and \( B \):
\[ \text{LCM}(A, B) \times \text{GCD}(A, B) = A \times B \]

### Step 2: Identify the known values.
In this case:
- \( \text{LCM} = 1056 \)
- One number \( A = 132 \)
- The other number \( B \) is unknown.
- Since both numbers are multiples of 12, their GCD will be 12.

### Step 3: Substitute the known values into the formula.
Substituting the known values into the formula gives:
\[ 1056 \times 12 = 132 \times B \]

### Step 4: Calculate the left-hand side.
First, calculate \( 1056 \times 12 \):
\[ 1056 \times 12 = 12672 \]

### Step 5: Set up the equation.
Now we have:
\[ 12672 = 132 \times B \]

### Step 6: Solve for \( B \).
To find \( B \), divide both sides by 132:
\[ B = \frac{12672}{132} \]

### Step 7: Perform the division.
Now, calculate \( \frac{12672}{132} \):
\[ B = 96 \]

### Conclusion:
Thus, the other number is \( 96 \).

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