If the product of two numbers is 1080 and their HCF is 30,
Question:

If the product of two numbers is 1080 and their HCF is 30, find their LCM.

Solution:

It is given that the product of two numbers is 1080.

Let the two numbers be a and b.

Therefore,

$a \times b=1080$

HCF is 30.

We need to find the LCM

We know that the product of two numbers is equal to the product of the HCF and LCM.

Thus,

$\mathrm{LCM}=\frac{a \times b}{\mathrm{HCF}}$

$\mathrm{LCM}=\frac{1080}{30}$

$\mathrm{LCM}=36$

Hence the LCM is 36