Question

The lcm of two numbers is 35322 if numbers are in ratio 1:3 then their hcf is

Answer 1

Solution :-

The  given two numbers are in the ratio of 1 : 3

Let the two numbers be x and 3x

Then, L.C.M. of  x and 3x is 3x (We know that the L.C.M. of 1 and 3 is 3. Hence L.C.M. of x and 3x is 3x).

It is given that the L.C.M. of x and 3x is 35322.

So, 3x = 35322

⇒ x = 35322/3

⇒ x =  11774

So, one of the two numbers is 11774.

Then, second number is 3*11774 = 35322

The two numbers are 11774 and 35322.

We know that,

L.C.M. × H.C.F. = Product of the two numbers

⇒ 35322 × H.C.F. = 11774 × 35322

⇒ H.C.F. = (11774 × 35322)/35322

⇒ H.C.F. = 11774

So, the H.C.F. of the given two numbers is 11774.

Answer.

Answer 2

Solution:

Given:
LCM = 35322

Let the two numbers be 1x & 3x

L.C.M. of 1x and 3x is 3x

3x = 35322

x = 35322/3

x = 11774

one of the two numbers is 11774.

second number is 3× 11774 = 35322

The two numbers are 11774 & 35322.


L.C.M. × H.C.F. = 1st number × 2nd number

35322 × H.C.F. = 11774 × 35322

H.C.F. = (11774 × 35322)/35322

H.C.F. = 11774

Hence, the H.C.F. of the two numbers is 11774.

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