Question

Two numbers are in the ratio 3:4. If their H.C.F. is 36, find :
(i) the numbers
(ii) their L.C.M.


$chapter \: name \: = \: hcf \: and \: lcm$
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Answer 1

Answer:

Numbers=108,144

LCM=432

Step-by-step explanation:

Let the numbers be 3x and 4x

HCF=36

HCF=x

Numbers= 3*36,4*36

= 108,144

LCM= 432

Answer 2

ANSWER:

Given:

• Ratio of 2 numbers = 3 : 4
• HCF = 36

To Find:

• the numbers
• their LCM

Solution:

We are given that,

⇒ Ratio of 2 numbers = 3 : 4

So,let the numbers be 3x and 4x respectively.

We know that, HCF of 2 numbers means the maximum number with which both the numbers can be completely divided.

Hence,

⇒ HCF of the numbers 3x and 4x = x

But, we are given that,

⇒ HCF = 36

So,

⇒ x = 36

Therefore, the numbers are:

• 3x = 3×36 = 108
• 4x = 4×36 = 144

The numbers are 108 and 144.

Now, we know that, for 2 numbers a and b,

⇒ a × b = HCF × LCM

Here, a = 108; b = 144; and HCF = 36

So,

⇒ 108 × 144 = 36 × LCM

⇒ LCM = (108 × 144)/36

⇒ LCM = 108 × 4

⇒ LCM = 432

The LCM of the numbers is 432.

The numbers are 108 and 144 respectively with LCM 432.

Formula Used:

• a × b = HCF × LCM