Question

The ratio of two numbers is 4: 5. If the hcf of these numbers is 6, what is their lcm

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Let the two numbers be 4x and 5x.

As 4 and 5 are coprime integers, the HCF of 4x and 5x is x.

Thus, x = 6.

And it is true that,

Product of two numbers = LCM × HCF

∴ LCM = Product of two numbers / HCF

The product of 4x and 5x is 20x².

Thus the LCM is

⇒ 20x² / x

⇒ 20x

⇒ 20 × 6

⇒ 120

Or the LCM method is given below.

$\begin{tabular}{l|l}x&4x,\ 5x \\ \cline{2-}&4,\ 5 \\ \cline{2-}\end{tabular} \\ \\ \\ \\ LCM=x \times 4 \times 5=20x \\ \\ \\ \\ 20x=20 \times 6=\bold{120}$

Thus the LCM is 120.

And the numbers are 24 and 30.