Two numbers are in ratio 2:5 and their HCF is 18. Their LCM is.

Options

A. 180
B. 36
C. 90
D. 188

Answer

To solve the problem, we need to find the LCM of two numbers that are in the ratio of 2:5 and have a given HCF of 18. Let's break this down step by step.

### Step 1: Define the Numbers
Given the ratio of the two numbers is 2:5, we can express the numbers as:
- First number = 2x
- Second number = 5x

### Step 2: Use the HCF to Find x
We know that the HCF of these two numbers is given as 18. Since the HCF is the common factor, we can set:
- HCF(2x, 5x) = x

Given that HCF = 18, we can equate:
- x = 18

### Step 3: Calculate the Actual Numbers
Now we can substitute the value of x back into the expressions for the numbers:
- First number = 2x = 2 * 18 = 36
- Second number = 5x = 5 * 18 = 90

### Step 4: Calculate the LCM
To find the LCM of two numbers, we can use the relationship between HCF and LCM:
\[ \text{LCM} \times \text{HCF} = \text{Product of the numbers} \]
So, we can calculate the LCM as follows:
\[ \text{LCM} = \frac{\text{Product of the numbers}}{\text{HCF}} = \frac{36 \times 90}{18} \]

### Step 5: Calculate the Product of the Numbers
Calculating the product:
\[ 36 \times 90 = 3240 \]

### Step 6: Divide by HCF
Now, we divide by the HCF:
\[ \text{LCM} = \frac{3240}{18} = 180 \]

### Final Answer
Thus, the LCM of the two numbers is **180**.

---