The HCF and LCM of two numbers are 30 and 2310 respectively. If first number is 330, the 2nd number is

Options

A. 231
B. 210
C. 200
D. 250

Answer

To find the second number when the HCF and LCM of two numbers are given, we can use the relationship between HCF, LCM, and the two numbers. The formula is:

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

Given:
- HCF = 30
- LCM = 2310
- First Number = 330
- Second Number = x (which we need to find)

### Step-by-Step Solution:

**Step 1:** Write down the relationship formula.
\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]

**Step 2:** Substitute the known values into the formula.
\[ 30 \times 2310 = 330 \times x \]

**Step 3:** Calculate the left side of the equation.
\[ 30 \times 2310 = 69300 \]

**Step 4:** Set up the equation.
\[ 69300 = 330 \times x \]

**Step 5:** Solve for x by dividing both sides by 330.
\[ x = \frac{69300}{330} \]

**Step 6:** Simplify the division.
- First, we can simplify \( \frac{69300}{330} \):
- Divide both the numerator and the denominator by 30:
\[ x = \frac{2310}{11} \]
- Now perform the division:
\[ x = 210 \]

**Final Answer:** The second number is 210.