Question

What is the LCM of \[2\] and \[4\]?

Answer 1

Hint: LCM or the least common multiple of two numbers is defined as the number which is divisible by both the numbers. There are two ways of finding both LCM and HCF. The first method is the division method and the second method is known as the prime factorization method. A co-prime number has HCF always one.

Complete step-by-step solution:
LCM stands for least common multiple. If we are finding LCM of two numbers then we are finding the least number which will be multiplied by both of them. If we are adding two numbers then LCM is used. If we are subtracting two numbers then also LCM is used. LCM is used for making the denominators common and it becomes easy to solve the questions of addition and subtraction.
There is one more term which is known as HCF. It stands for the highest common factor. HCF is defined as the largest factor of any two given numbers. If there are two or more numbers and if we are finding their HCF then their HCF will not be greater than any of the given numbers. Also, the LCM of two or more numbers will never be greater than any of the given numbers.
There are various properties related to HCF and LCM.
The first one is that the product of HCF and LCM of two given numbers will be equal to the product of the given two numbers which is as shown below.
\[LCM\times HCF=product\text{ }of\text{ }numbers\]
We know that the HCF of a co-prime number is \[1\] therefore the LCM of given co-prime numbers will be equal to the product of co-prime numbers.
In the above question, we have to find the LCM of\[2\] and \[4\]. Firstly we will find the factors of \[2\] and then we will find the factors of \[4\].
\[2=1\times 2\]
\[4=2\times 2\times 1\]
After calculating the factors of both the numbers, multiply the factors maximum number of times it occurs in the number. Suppose \[2\] occurs two times in the number so it will be multiplied two times and hence the LCM will be.
\[LCM(\text{2 and 4})=2\times 2\times 1\]
So the LCM will be \[4\].

Note: HCF is also known as the greatest common divisor and LCM is also known as the smallest common multiple. Prime numbers are those numbers that are not divisible by any number other than one and the number itself and co-prime numbers are those numbers that do not have any common factor between them