Question

Find LCM of numbers $72,108$ and $2100$.

Answer 1

Express the given numbers as the product of their prime factors to find the LCM :

Given numbers, $72,108$ and $2100$

$\begin{array}{rcl}72& =& 2\times 2\times 2\times 3\times 3=2^3\times 3^2\\ 108& =& 2\times 2\times 3\times 3\times 3=2^2\times 3^3\\ 2100& =& 2\times 2\times 3\times 5\times 5\times 7=2^2\times 3^1\times 5^2\times 7^1\end{array}$

LCM can be calculated as the product of the prime factors raised to their highest power

$\therefore$ $LCM=2^3\times 3^3\times 5^2\times 7^1$

$=8\times 27\times 25\times 7$

$\therefore$ $LCM=37800$

Hence the LCM of $72,108$ and $2100$ is $37800$