Each question has four options(A), (B), (C) and (D) for answers. Select the right answer and write in English letters in the box against each question in the enclosed answer sheet.
Two numbers are in the ratio 5 : 6. If their H.C.F is 4, then their L.C.M. will be

Options

A. 90
B. 96
C. 120
D. 150

Answer

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

### Step 1: Understand the Ratio and HCF
The two numbers are in the ratio of 5:6. This means we can express the two numbers as:
- First number = 5x
- Second number = 6x
where x is a common multiplier.

### Step 2: Use the HCF
We are given that the HCF (Highest Common Factor) of these two numbers is 4. This means that:
- 5x and 6x must both be multiples of 4.

Since the HCF is 4, we can say:
- x = 4 (because the HCF must be a factor of both numbers).

### Step 3: Calculate the Numbers
Now, substituting x = 4 into the expressions for the numbers:
- First number = 5x = 5 * 4 = 20
- Second number = 6x = 6 * 4 = 24

### Step 4: Calculate the LCM
Now we need to find the LCM (Lowest Common Multiple) of the two numbers, 20 and 24. The formula relating HCF and LCM is:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

Using the values we have:
- HCF = 4
- Product of the two numbers = 20 * 24 = 480

Now we can rearrange the formula to find LCM:
\[ \text{LCM} = \frac{\text{Product of the two numbers}}{\text{HCF}} \]

Substituting the known values:
\[ \text{LCM} = \frac{480}{4} = 120 \]

### Final Answer
Thus, the LCM of the two numbers is 120.