Answer
The greatest common divisor of two or more natural numbers can be obtained by finding out the largest number that divides both the natural numbers.
The least common multiple of two or more natural numbers is the smallest number that is divisible by both/all the natural numbers.
Although, the process for finding both GCD and LCM is same, yet they differ in terms of grouping the factors.
In GCD, common factors from both the numbers are taken, whereas in LCM, greater exponent factors are taken from both the numbers.
For example, take two numbers 48 and 72.
Factors of 48 can be written as,
\[\begin{align}
& 48=2\times 2\times 2\times 3\times 2 \\
& ={{2}^{4}}\times 3
\end{align}\]
and, factors of 72 can be written as:
\[\begin{align}
& 72=2\times 2\times 2\times 3\times 3 \\
& ={{2}^{3}}\times {{3}^{2}}
\end{align}\]
To find GCD, take the common factors from both the numbers. Thus,
\[\begin{align}
& \text{GCD=}{{\text{2}}^{3}}\times 3 \\
& =2\times 2\times 2\times 3 \\
& =24
\end{align}\]
Hence, greatest common divisor of 48 and 72 is 24.
