Question

What is the LCM of 10 and 4?

Answer 1

Hint: In the above mentioned question we need to find the LCM which means the least common factor between 10 and 4 in this we will factorize both the terms and we are going to use the common terms once and we are also going to use the uncommon terms to find the LCM between the terms mentioned, then we are going to multiply all the factors and the resultant number will be regarded as the LCM of the two numbers.

Complete step by step solution:
In the above mentioned question where we need to find LCM between two numbers we will first understand what LCM is, as the name suggests this is the least common factor between two numbers which can be taken out with the help of factors of those two terms. Once we are done with the factorization of both the terms we will then select the common terms once and then select the uncommon terms in the factorization to get our LCM of the given two numbers. So in the above question we have 10 and 4 as our terms now when we factorize both of them we will get the factorization as:
\[10=2\times 5\]
\[4=2\times 2\]
In the above two factorization we can clearly see that one factor is common i.e. 2 so we are going to consider it one time and the remaining factors i.e. 2 and 5 are not common so they will also be taken for calculating LCM of the given numbers with which we will get our LCM as:
\[LCM=2\times 2\times 5\]
\[LCM=20\]
So we get the LCM of the two terms i.e. 10 and 4 as 20.

Note: In the above type of question there is also a short method to calculate LCM of the two numbers i.e. when the given two numbers are prime so the LCM of the two numbers will be the product of two numbers so with this is how we can calculate the LCM of two prime numbers without calculating its factors.