Question 4

The product of two numbers is equal to the product of their HCF and LCM.

Step 1 — Identify Given Values

We are given two numbers. Let's call them a and b. So, a = 306. And b = 657. We are also given their HCF. HCF (306, 657) = 9.

Step 2 — Calculate LCM

Let's use the relationship between HCF, LCM, and the numbers. We know the formula: $\text{LCM} \times \text{HCF} = \text{Product of the two numbers}$ We can rearrange this formula to find the LCM. $\text{LCM} = \frac{\text{Product of the two numbers}}{\text{HCF}}$ Now, let's substitute the given values into the formula. $\text{LCM} = \frac{306 \times 657}{9}$ Let's perform the multiplication in the numerator first. $\text{LCM} = \frac{201042}{9}$ Now, we perform the division. $\text{LCM} = 22338$

$\boxed{\text{LCM} (306, 657) = 22338}$

Answer

(i) The LCM (306, 657) is 22338.