The LCM of two numbers is 693 and their HCF is 11. One of the number is 77, the other number is

Options

A. 66
B. 35
C. 99
D. 68

Answer

To find the other number given the LCM, HCF, and one of the numbers, we can use the relationship between LCM, HCF, and the two numbers. Here’s the step-by-step solution:

### Step 1: Understand the relationship
We know that:
\[ \text{LCM} \times \text{HCF} = \text{Number 1} \times \text{Number 2} \]
Where:
- LCM = 693
- HCF = 11
- Number 1 = 77
- Number 2 = x (the unknown number)

### Step 2: Substitute the known values
Substituting the known values into the equation gives us:
\[ 693 \times 11 = 77 \times x \]

### Step 3: Calculate the left side
Now, calculate \(693 \times 11\):
\[ 693 \times 11 = 7623 \]

### Step 4: Set up the equation
Now we have:
\[ 7623 = 77 \times x \]

### Step 5: Solve for x
To find x, divide both sides by 77:
\[ x = \frac{7623}{77} \]

### Step 6: Perform the division
Now, calculate \(7623 \div 77\):
\[ x = 99 \]

### Conclusion
The other number is:
\[ \text{Number 2} = 99 \]

### Final Answer
The other number is **99**.

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