Question

. The two given numbers a and b are in the ratio 5:6 such that their lcm is 480. Find their hcf.

Answer 1

$5 x\times 6x = 480 \times x \\ 30x = 480 \\ x = \frac{480}{30} \\ x = 16$

Answer 2

Given:

Two numbers in the ratio of 5:6

Their L.C.M is 480

To Find:

Their H.C.F

Solution:

Let us take the numbers 5x and 6x

L.C.M of two numbers is the Least Common Multiple and H.C.F is the Highest Common Factor.

Also,

''The product of L.C.M and H.C.F is equal to the product of two numbers''

Now,

According to question

The product of two numbers = (5x)×(6x)

Where x is the H.C.F

Also the L.C.M of the two numbers = 480

So,

L.C.M×H.C.F =  (5x)×(6x)

⇒480 × H.C.F = 30x²

⇒480×x =  30x²

⇒x = 480/30

⇒x = 16

Hence, the H.C.F of the two numbers is 16.