The lowest common multiple of X and 12 is 120. The highest common factor of X and 12 is four find X.

We are given:

- The lowest common multiple (LCM) of \( X \) and 12 is 120.
- The highest common factor (HCF) of \( X \) and 12 is 4.

We can use the relationship between the LCM, HCF, and the two numbers:

\[
\text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b
\]

For \( X \) and 12, this becomes:

\[
\text{LCM}(X, 12) \times \text{HCF}(X, 12) = X \times 12
\]

Substitute the known values:

\[
120 \times 4 = X \times 12
\]

Simplify:

\[
480 = 12X
\]

Now solve for \( X \):

\[
X = \frac{480}{12} = 40
\]

Thus, \( X = 40 \).

Would you like more details or further clarification on this?

Here are 5 related questions to explore further:

1. How do you calculate the LCM of two numbers?
2. What is the relationship between HCF and LCM?
3. How can you find the HCF of two numbers using prime factorization?
4. How would you find the LCM if \( X \) and 12 were different numbers?
5. How do we check if a number is divisible by another?

**Tip:** When solving LCM and HCF problems, always remember their fundamental relationship with the product of the numbers involved!

The lowest common multiple of X and 12 is 120. The highest common factor of X and 12 is 4. Find X.

Learn how to find the value of X given that the LCM of X and 12 is 120 and the HCF is 4. This problem involves the relationship between the Lowest Common Multiple and the Highest Common Factor, with a step-by-step explanation. Suitable for students in Grades 6-8.

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