**HCF** (Highest Common Factor) and **LCM** (Lowest Common Multiple) are important concepts in mathematics. The HCF is the largest number that divides two given numbers without leaving a remainder, while the LCM is the smallest number that is a multiple of both given numbers.

Let's solve the problem step by step:

**Step 1: Finding the HCF**

Given that the HCF of the two numbers is 18, we need to find two numbers whose HCF is 18.

We can write the two numbers as:
Number 1 = 18a
Number 2 = 18b

Where 'a' and 'b' are any positive integers.

Since the product of the two numbers is 1620, we can write the equation:
18a * 18b = 1620

Simplifying the equation, we get:
ab = 90

Now, we need to find the factors of 90. The factors of 90 are:
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Among these factors, the only pair that satisfies the equation ab = 90 is a = 9 and b = 10.

Therefore, the two numbers are:
Number 1 = 18 * 9 = 162
Number 2 = 18 * 10 = 180

So, the HCF of the two numbers is 18.

**Step 2: Finding the LCM**

To find the LCM of two numbers, we can use the formula:
LCM = (Number 1 * Number 2) / HCF

Substituting the values, we get:
LCM = (162 * 180) / 18
= 29160 / 18
= 1620

Therefore, the LCM of the two numbers is 1620.

In conclusion, given that the HCF of two numbers is 18 and their product is 1620, the LCM of the two numbers is also 1620.

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