The H.C.F. And L.C.M. of two numbers are 44 and 264 respectively . If the first number is dividded by2, the quotient is 44, The other numbes is

Options

A. 147
B. 528
C. 132
D. 264

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the first number
The problem states that when the first number is divided by 2, the quotient is 44. Therefore, we can find the first number by multiplying the quotient by 2.

\[ \text{First Number} = 44 \times 2 = 88 \]

### Step 2: Use the relationship between HCF, LCM, and the product of the numbers
We know that the product of the two numbers is equal to the product of their HCF and LCM. This can be expressed as:

\[ \text{First Number} \times \text{Second Number} = \text{HCF} \times \text{LCM} \]

Substituting the known values:

\[ 88 \times \text{Second Number} = 44 \times 264 \]

### Step 3: Calculate the product of HCF and LCM
Now we calculate the right side of the equation:

\[ 44 \times 264 = 11616 \]

### Step 4: Solve for the second number
Now we can substitute this value back into the equation to find the second number:

\[ 88 \times \text{Second Number} = 11616 \]

To find the second number, we divide both sides by 88:

\[ \text{Second Number} = \frac{11616}{88} \]

### Step 5: Perform the division
Now we perform the division:

\[ \text{Second Number} = 132 \]

### Final Answer
Thus, the second number is **132**.

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