The H.C.F. and L.C.M. of two numbers are 12 and 336 respectively. If one of the number is 84 then the other be:

Options

A. a. 36
B. b. 48
C. c. 72
D. d. 96

Answer

To find the other number when given the H.C.F. and L.C.M. of two numbers, we can use the relationship between these three quantities. The relationship states that:

\[ \text{H.C.F.} \times \text{L.C.M.} = \text{Product of the two numbers} \]

Given:
- H.C.F. = 12
- L.C.M. = 336
- One number (let's call it \( a \)) = 84

Let the other number be \( b \).

### Step 1: Set up the equation using the relationship
Using the relationship mentioned above, we can write:

\[ 12 \times 336 = 84 \times b \]

### Step 2: Calculate the left side of the equation
Now, let's calculate \( 12 \times 336 \):

\[ 12 \times 336 = 4032 \]

### Step 3: Substitute the value into the equation
Now substitute this value back into the equation:

\[ 4032 = 84 \times b \]

### Step 4: Solve for \( b \)
To find \( b \), we can rearrange the equation:

\[ b = \frac{4032}{84} \]

### Step 5: Perform the division
Now, let's perform the division:

\[ b = 48 \]

### Conclusion
Thus, the other number is \( 48 \).