The LCM of two numbers is 2079 and their HCF is 27. If one of the numbers is 189, what is the other number?

Use the relation:

Product of two numbers = LCM × HCF

Step 1:

Let the other number be $x$

$189 \times x = 2079 \times 27$

Step 2:

$x = \frac{2079 \times 27}{189}$

Since $189 = 27 \times 7$,

$x = \frac{2079 \times 27}{27 \times 7} = \frac{2079}{7}$

Step 3:

$x = 297$