We are given the HCF (highest common factor) and LCM (least common multiple) of two numbers, and one of the numbers. We need to find the other number. Specifically, the HCF is 12, the LCM is 3780, and one number is 84.

1. Problem Description

We are given the HCF (highest common factor) and LCM (least common multiple) of two numbers, and one of the numbers. We need to find the other number. Specifically, the HCF is 12, the LCM is 3780, and one number is

8

4.

2. Solution Steps

Let the two numbers be $a$ and $b$. We are given that HCF$(a, b) = 12$, LCM$(a, b) = 3780$, and $a = 84$. We need to find $b$. We know that the product of two numbers is equal to the product of their HCF and LCM.

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

Substituting the given values, we get

$$84 \times b = 12 \times 3780$$

$$b = \frac{12 \times 3780}{84}$$

$$b = \frac{12 \times 3780}{12 \times 7}$$

$$b = \frac{3780}{7}$$

$$b = 540$$

3. Final Answer

The other number is 540.