 If HCF (6, a) = 2 and LCM (6, a) = 60, then find a.

Given the conditions:
- \(\text{HCF}(6, a) = 2\)
- \(\text{LCM}(6, a) = 60\)

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

\[
\text{HCF}(6, a) \times \text{LCM}(6, a) = 6 \times a
\]

Substituting the known values:

\[
2 \times 60 = 6 \times a
\]

Simplifying this:

\[
120 = 6a
\]

Dividing both sides by 6:

\[
a = \frac{120}{6} = 20
\]

So, the value of \(a\) is \(20\).

Would you like further details on this process or have any questions?

Here are 5 related questions you might find interesting:
1. How do you find the HCF of two numbers using the prime factorization method?
2. What is the relationship between HCF and LCM for any two numbers?
3. Can the HCF of two numbers ever be greater than the smallest number?
4. How do you calculate the LCM of two numbers using their prime factors?
5. What happens to the LCM if one of the numbers is a multiple of the other?

**Tip:** When working with HCF and LCM, remember that their product is always equal to the product of the two numbers themselves.

Learn how to find the value of 'a' given that HCF(6, a) = 2 and LCM(6, a) = 60. This problem explores key number theory concepts including HCF and LCM relationships, suitable for Grades 7-9 mathematics students.

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