The HCF and LCM of two numbers are 5 and 140, respectively. If one of the number is 35, then find the another number.

Options

A. 10
B. 15
C. 18
D. 20

Answer

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

### Step 1: Write down the given values
- HCF = 5
- LCM = 140
- One number (let's call it A) = 35

### Step 2: Use the relationship between HCF, LCM, and the two numbers
The relationship states that:
\[ \text{HCF} \times \text{LCM} = A \times B \]
where A and B are the two numbers.

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 5 \times 140 = 35 \times B \]

### Step 4: Calculate the left side of the equation
Calculating the left side:
\[ 5 \times 140 = 700 \]
So, we have:
\[ 700 = 35 \times B \]

### Step 5: Solve for B
To find B, divide both sides of the equation by 35:
\[ B = \frac{700}{35} \]

### Step 6: Perform the division
Calculating the division:
\[ B = 20 \]

### Conclusion
The other number is **20**.

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