The ratio of two numbers is 5:6 and their LCM is 150. Find the sum of the two numbers.

Options

A. 50
B. 55
C. 60
D. 54

Answer

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

### Step 1: Understand the ratio
The ratio of the two numbers is given as 5:6. This means we can express the two numbers in terms of a variable \( x \):
- First number = \( 5x \)
- Second number = \( 6x \)

### Step 2: Use the LCM
We are given that the LCM of these two numbers is 150. The LCM of \( 5x \) and \( 6x \) can be calculated as follows:
- The LCM of \( 5 \) and \( 6 \) is \( 30 \).
- Therefore, the LCM of \( 5x \) and \( 6x \) is \( 30x \).

### Step 3: Set up the equation
Since we know the LCM is 150, we can set up the equation:
\[ 30x = 150 \]

### Step 4: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 30:
\[ x = \frac{150}{30} = 5 \]

### Step 5: Find the two numbers
Now that we have \( x \), we can find the two numbers:
- First number = \( 5x = 5 \times 5 = 25 \)
- Second number = \( 6x = 6 \times 5 = 30 \)

### Step 6: Calculate the sum of the two numbers
Now, we can find the sum of the two numbers:
\[ \text{Sum} = 25 + 30 = 55 \]

### Final Answer
The sum of the two numbers is **55**.

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