The L.C.M. of two numbers is 1820 and their H.C.F. is 26. If one number is 130 then the other number is :

Options

A. 70
B. 1690
C. 364
D. 1264

Answer

To find the other number when given the LCM, HCF, and one of the numbers, we can use the relationship between these values. Here’s the step-by-step solution:

### Step 1: Understand the relationship between LCM, HCF, and the two numbers.
The relationship is given by the formula:
\[ \text{LCM} \times \text{HCF} = \text{Number 1} \times \text{Number 2} \]

### Step 2: Identify the known values.
From the question, we have:
- LCM = 1820
- HCF = 26
- Number 1 = 130
- Number 2 = X (the unknown we need to find)

### Step 3: Substitute the known values into the formula.
Using the formula from Step 1:
\[ 1820 \times 26 = 130 \times X \]

### Step 4: Calculate the left side of the equation.
First, calculate \(1820 \times 26\):
\[ 1820 \times 26 = 47320 \]

### Step 5: Set up the equation.
Now we have:
\[ 47320 = 130 \times X \]

### Step 6: Solve for X.
To find X, divide both sides by 130:
\[ X = \frac{47320}{130} \]

### Step 7: Perform the division.
Calculating \( \frac{47320}{130} \):
\[ X = 364 \]

### Conclusion:
The other number is \(364\).

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