Question

The ratio of two numbers is 3:4 and their H.C.F is 4, their L.C.M is
A) 12
B) 16
C) 24
D) 48

Answer 1

Hint: Here we are asked to find out H.C.F that is the highest common factor and another thing we have to find out is L.C.M that is the lowest common factor. So, we will first take the lowest number that is divisible by each of three numbers. After that the next number that is divisible by at least two numbers and so on.
 Formula used:
HCF X L.C.M= Product of two numbers

Complete step-by-step answer:
Here we are given with ratio of two numbers as 3:4 and their H.C.F as 4
We are asked to find the L.C.M of the number
So basically H.C.F is the highest common factor of both the numbers. So, two numbers can have many factors in common so the highest among the factors will be the H.C.F of the numbers whereas the L.C.M is known as Lowest common multiple. Hence, we will take the multiples of both the numbers and find the lowest multiple which belongs to both the numbers. Because there will be infinitely many numbers of multiples for a single number. So, we will find it accordingly.
We have a formula HCF X L.C.M= Product of two numbers
Hence, we will execute this formula to find the L.C.M of both the numbers.
Since the numbers are given in the ratio $3:4$
And we have given that the H.C.F is 4
So, let’s take the numbers as 3x and 4x respectively
As H.C.F is 4 hence the numbers will be $3\times 4=12$ and $4\times 4=16$ respectively
Now we have both the numbers that are 12 and 16 so the product of both the numbers is
$12\times 16= 192$
Hence now we have H.C.F x L.C.M=192
 So, $4 \times L.C.M=192$
 $ \Rightarrow L.C.M = \dfrac{{192}}{4} = 48 $
Hence, we have L.C.M of the numbers 12 and 16 as 48.
So, corresponding to this we have option D hence option D is the correct answer.
So, the correct answer is “Option D”.

Note: If we have any two prime numbers then their H.C.F will be 1 and L.C.M will be product of both the numbers. If the L.C.M of two numbers is ‘1’ then the two numbers are called co-primes w.r.t each other.