The ratio of two positive numbers is 11: 17 and their HCF is 4. Their LCM is:

Let's solve this problem step by step.

Given:
- The ratio of two numbers is 11:17.
- The Highest Common Factor (HCF) of the two numbers is 4.

Let's denote the two numbers as \( 11x \) and \( 17x \), where \( x \) is a common factor.

### Step 1: Calculate the two numbers
Since the HCF of the two numbers is 4, we can express the numbers as:
\[
\text{Number 1} = 11x
\]
\[
\text{Number 2} = 17x
\]
Given that the HCF is 4, \( x = 4 \). Thus, the two numbers are:
\[
\text{Number 1} = 11 \times 4 = 44
\]
\[
\text{Number 2} = 17 \times 4 = 68
\]

### Step 2: Calculate the LCM
The LCM (Least Common Multiple) of two numbers \( a \) and \( b \) can be found using the formula:
\[
\text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)}
\]
Substituting the values:
\[
\text{LCM}(44, 68) = \frac{44 \times 68}{4} = \frac{2992}{4} = 748
\]

Thus, the LCM of the two numbers is **748**.

Would you like more details or have any questions? Here are some related questions:

1. What is the relationship between HCF and LCM?
2. How do you find the HCF of two numbers?
3. Can the LCM of two numbers ever be smaller than both numbers?
4. What are the properties of numbers with a ratio of 11:17?
5. How can you check if two numbers are co-prime?

**Tip:** When dealing with ratios, remember that the numbers are multiples of the ratio, scaled by a common factor.

Solve the problem of finding the LCM of two numbers given their ratio 11:17 and HCF as 4. This step-by-step solution covers essential concepts like ratio, GCD, and LCM, suitable for students in Grades 6-8.

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