If the ratio of two numbers is 3:4 and their LCM is 84 then find the larger number.

Options

A. 21
B. 28
C. 24
D. 84

Answer

To solve the problem, we need to follow these steps:

### Step 1: Understand the given ratio
The ratio of the two numbers is given as 3:4. We can represent the two numbers in terms of a variable \( x \):
- Let the first number be \( 3x \)
- Let the second number be \( 4x \)

### Step 2: Use the information about the LCM
We are given that the least common multiple (LCM) of these two numbers is 84. The LCM of \( 3x \) and \( 4x \) can be calculated as follows:
- The LCM of \( 3 \) and \( 4 \) is \( 12 \).
- Therefore, the LCM of \( 3x \) and \( 4x \) is \( 12x \).

### Step 3: Set up the equation
Since we know the LCM is 84, we can set up the equation:
\[ 12x = 84 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 12:
\[ x = \frac{84}{12} = 7 \]

### Step 5: Find the two numbers
Now that we have \( x \), we can find the two numbers:
- First number: \( 3x = 3 \times 7 = 21 \)
- Second number: \( 4x = 4 \times 7 = 28 \)

### Step 6: Identify the larger number
The larger number between \( 21 \) and \( 28 \) is:
\[ \text{Larger number} = 28 \]

### Final Answer
Thus, the larger number is **28**.

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