If LCM and HCF of the two numbers are given by 1105 and 5 respectively. One of the numbers is 65. Find the second number.

Options

A. 85
B. 81
C. 95
D. 72

Answer

To find the second number when the LCM and HCF of two numbers are given, we can use the relationship between these values. The product of the two numbers is equal to the product of their LCM and HCF.

**Step 1: Write down the relationship.**
The formula we will use is:
\[ \text{Product of two numbers} = \text{LCM} \times \text{HCF} \]

**Step 2: Substitute the known values.**
We know:
- LCM = 1105
- HCF = 5
- One number (let's call it A) = 65

Let the second number be B. Therefore, we can write:
\[ A \times B = \text{LCM} \times \text{HCF} \]
Substituting the known values:
\[ 65 \times B = 1105 \times 5 \]

**Step 3: Calculate the right-hand side.**
First, calculate \(1105 \times 5\):
\[ 1105 \times 5 = 5525 \]
Now, we have:
\[ 65 \times B = 5525 \]

**Step 4: Solve for B.**
To find B, divide both sides by 65:
\[ B = \frac{5525}{65} \]

**Step 5: Perform the division.**
Now, let's simplify \( \frac{5525}{65} \):
- First, divide the numerator and denominator by 5:
\[ \frac{5525 \div 5}{65 \div 5} = \frac{1105}{13} \]
Now, perform the division:
\[ 1105 \div 13 = 85 \]

Thus, the second number B is:
\[ B = 85 \]

**Final Answer:**
The second number is 85.

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