Question

A6 (B4 The ratio of two numbers is 3:4 and their H.C.F is 4. What is their L.C.M.? (A) 12 (B) 16 (C) 24 (D) 48 ​

Answer 1

Answer:

48 (Option D)

Step-by-step explanation:

Let the numbers be 3x and 4x.

Then, their HCF =x

Given that their H.C.F is 4

So, x=4  

So, the numbers are 3x=12 and 4x=16.

LCM of 12 and 16 is 48.

Answer 2

Given data,

The ratio of two numbers is $3:4$

Let the two numbers be $3x,4x$

HCF of the given numbers is $4$

As we know that the HCF is the multiple of given numbers,

Then we can take $x=4$

Substitute the value of $x$ in $3x,4x$

We get,

$3x=3(4)=12$

$4x=4(4)=16$

The two numbers are $12,16$

As we know that the formula related to both LCM and HCF is,

Product of two numbers = LCM $\times$ HCF

$12\times16=LCM \times 4$

$LCM=\frac{12\times16}{4}$

$LCM=12\times4$

$LCM=48$

Therefore, LCM of  $12,16$ is $48$