If ratio and HCF of two numbers are 3 : 4 and 5 respectively. Then find the LCM ?

Options

A. 10
B. 60
C. 15
D. 12

Answer

To find the LCM of two numbers given their ratio and HCF, we can follow these steps:

### Step 1: Understand the Given Information
We are given:
- The ratio of two numbers is 3:4.
- The HCF (Highest Common Factor) of the two numbers is 5.

### Step 2: Express the Numbers in Terms of a Variable
Let the two numbers be represented as:
- First number = 3x
- Second number = 4x

Here, 'x' is a common factor that we will determine.

### Step 3: Relate HCF to the Expression
Since we know that the HCF of the two numbers is 5, we can set up the equation:
- HCF(3x, 4x) = x = 5

### Step 4: Solve for x
From the equation above, we can find the value of x:
- x = 5

### Step 5: Substitute x Back to Find the Numbers
Now, we can substitute x back into our expressions for the numbers:
- First number = 3x = 3 * 5 = 15
- Second number = 4x = 4 * 5 = 20

### Step 6: Calculate the LCM
We know the relationship between LCM, HCF, and the product of the two numbers:
\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]
Substituting the values we have:
\[ \text{LCM} \times 5 = 15 \times 20 \]
\[ \text{LCM} \times 5 = 300 \]

### Step 7: Solve for LCM
Now, we can solve for LCM:
\[ \text{LCM} = \frac{300}{5} = 60 \]

### Conclusion
The LCM of the two numbers is **60**.

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