The LCM of two number is `20^(th)` multiple of 3. HCF of those two numbers is 6. If one number is 30, what is another number?

Options

A. 16
B. 14
C. 12
D. 10

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the given information
We are given:
- LCM of two numbers = 20th multiple of 3 = 20 × 3 = 60
- HCF of the two numbers = 6
- One of the numbers = 30

### Step 2: Use the relationship between LCM, HCF, and the two numbers
The relationship between LCM, HCF, and the two numbers can be expressed with the formula:
\[ \text{LCM} \times \text{HCF} = \text{First Number} \times \text{Second Number} \]

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 60 \times 6 = 30 \times \text{Second Number} \]

### Step 4: Calculate the left side of the equation
Calculating the left side:
\[ 60 \times 6 = 360 \]
So, we have:
\[ 360 = 30 \times \text{Second Number} \]

### Step 5: Solve for the Second Number
To find the Second Number, we can rearrange the equation:
\[ \text{Second Number} = \frac{360}{30} \]

### Step 6: Perform the division
Now, performing the division:
\[ \text{Second Number} = 12 \]

### Conclusion
The other number is **12**.

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