Question

Find the LCM of $12$ and $4$.

Answer 1

Hint:In this question we have to find the LCM of the given numbers. So for finding the least common multiple or LCM we will use the Prime factorisation method of the given set. We will find the prime factors or multiples of the given number and then we will use the product of those numbers that have the highest numbers of powers in them.

Complete step by step answer:
We should know that the least common multiple is a set of numbers that is defined as the smallest possible number which is divisible by all the given numbers in that set. So to find the LCM, we first factorise the numbers i.e. we write all the numbers as the product of the prime numbers. And then we calculate the LCM.Here we have $12$ and $4$ .

We will write the first number as a product of prime numbers i.e.
$12 = 2 \times 2 \times 3$ .
It can also be written as
$12 = {2^2} \times {3^1}$
Now in the second number, we have:
$4 = 2 \times 2$
$\Rightarrow 4 = {2^2}$
We can see that the highest occurrence or power of $2$ is $2$ times, and that of $3$ is $1$ time. So we can say that
$LCM(12,4) = {2^2} \times 3$
It gives us $4 \times 3 = 12$

Hence the required LCM is $12$.

Note: We should note that Prime numbers are those numbers that are divisible by one and itself. As for example: $2,3,5,7,19,23...$ are prime numbers. We should know the formula to calculate the LCM.The formula for calculating the LCM of any two numbers is
$\dfrac{{x \times y}}{{HCF(x,y)}}$ , where $x,y$ are two integers. And we divide the product with HCF or the highest common factor of both the numbers. Similarly the formula for calculating the LCM of fractions is $\dfrac{{L.C.M\,of\,Numerator}}{{H.C.F\,of\,Denominator}}$.