Question

What is the lowest common multiple of \[12\] and \[21\]?

Answer 1

Hint: In the given question, we are asked to find the LCM or the Lowest Common Multiple of two given numbers \[12\] and \[21\]. We will first find the factors of the two numbers given to us. Then, from those factors we will select those terms which are not common to both the numbers and if there are any common terms in the numbers involved, then, we will use that common term only once. After taking all the required terms out, we will multiply the terms and will get the required LCM of the given numbers.

Complete step-by-step solution:
According to the given question, we are asked to find the LCM of the given numbers.
LCM or Lowest Common Multiple of two numbers can be said to be the lowest multiple of the both the numbers involved which is common to both of them and is divisible by the numbers.
We are given \[12\] and \[21\],
Firstly, we will find the factors of the numbers given to us. So, we have,
\[12=2\times 2\times 3\]
\[21=3\times 7\]
To get the LCM, we have to choose those factors which are not at all common to both the numbers. If a factor is common to both the numbers then, we will take that factor only once.
We can see in the above factors of the numbers, that, only 3 is common to both the numbers. So, we will be taking 3 only once in the LCM. Rest all the numbers are taken as it is since those factors are not common to both the numbers involved.
We get the LCM as,
\[LCM(12,21)=2\times 2\times 3\times 7\]
\[\Rightarrow LCM(12,21)=84\]
Therefore, the LCM of \[12\] and \[21\] is \[84\].

Note: The LCM and HCF are two different concepts. Maximum mistakes are done because of the confusion between LCM and HCF. LCM refers to Lowest Common Multiple and HCF refers to Highest Common Factor or Greatest Common Divisor (GCD).
If LCM of \[12\] and \[21\] is \[84\],
Then the HCF \[12\] and \[21\] is 3, as 3 is the only common factor between the two numbers.