Question

Find the LCM of: $4,5\,\,and\,\,6$.

Answer 1

Hint: LCM of a group of numbers is the smallest number that is a multiple of all the numbers. We will do prime factorization of $4,5\,\,and\,\,6$ simultaneously to get the desired result.

Complete step by step solution:
Now, we will do prime factorization of $4,5\,\,and\,\,6$ simultaneously

$2$	$4 - 5 - 6$
$2$	$2 - 5 - 3$
$3$	$1 - 5 - 3$
$5$	$1 - 5 - 1$
	$1 - 1 - 1$

So, $ = 2 \times 2 \times 3 \times 5$
$ = 4 \times 3 \times 5$
$ = 12 \times 5$
$ = 60$
Hence, LCM of $4,5\,\,and\,\,6$ is $60$

Note: Prime factor is the factor of the given number which is the prime number. Factors are the numbers which we multiply together to get another number.
We can also find LCM of these numbers by using the factor tree method.




\[
  4 = 2 \times 2 \\
  5 = 1 \times 5 \\
  6 = 2 \times 3 \\
 \]
From the above figure, we can take the pair of common factors and unique factors from the branches of both the numbers and multiply them as a whole to get the LCM.
So, LCM \[(4,5,6) = 2 \times 2 \times 3 \times 5\]
LCM\[(4,5,6) = 60\]