The sum of the HCF and LCM of two numbers is 496 their LCM is 15 times their HCF. If one number is 93, then find the another number is

Options

A. 155
B. 122
C. 124
D. 138

Answer

To solve the problem step by step, we need to find the second number given the HCF and LCM conditions. Let's break it down:

### Step 1: Understand the given information
We know:
- The sum of the HCF (let's denote it as H) and LCM (let's denote it as L) of two numbers is 496.
- The LCM is 15 times the HCF.
- One of the numbers is 93.

### Step 2: Set up the equations
From the problem, we can set up the following equations:
1. \( H + L = 496 \) (Equation 1)
2. \( L = 15H \) (Equation 2)

### Step 3: Substitute Equation 2 into Equation 1
Substituting \( L \) from Equation 2 into Equation 1 gives us:
\[ H + 15H = 496 \]
\[ 16H = 496 \]

### Step 4: Solve for H
Now, divide both sides by 16:
\[ H = \frac{496}{16} \]
\[ H = 31 \]

### Step 5: Find L
Now that we have H, we can find L using Equation 2:
\[ L = 15H = 15 \times 31 = 465 \]

### Step 6: Use the relationship between HCF, LCM, and the two numbers
We know that:
\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]
Substituting the values we have:
\[ 31 \times 465 = 93 \times \text{Second Number} \]

### Step 7: Calculate the left-hand side
Calculating \( 31 \times 465 \):
\[ 31 \times 465 = 14415 \]

### Step 8: Set up the equation for the second number
Now we have:
\[ 14415 = 93 \times \text{Second Number} \]

### Step 9: Solve for the Second Number
To find the second number, divide both sides by 93:
\[ \text{Second Number} = \frac{14415}{93} \]
Calculating this gives:
\[ \text{Second Number} = 155 \]

### Conclusion
The second number is **155**.

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