Finding LCM of more than two (or array) numbers without using GCD

Given an array of positive integers, find LCM of the elements present in array.
Examples: 
 

Input : arr[] = {1, 2, 3, 4, 28}
Output : 84

Input : arr[] = {4, 6, 12, 24, 30}
Output : 120

 

We have discussed LCM of array using GCD.
In this post a different approach is discussed that doesn't require computation of GCD. Below are steps. 
 

1. Initialize result = 1
2. Find a common factors of two or more array elements.
3. Multiply the result by common factor and divide all the array elements by this common factor.
4. Repeat steps 2 and 3 while there is a common factor of two or more elements.
5. Multiply the result by reduced (or divided) array elements.

Illustration : 

Let we have to find the LCM of 
arr[] = {1, 2, 3, 4, 28}

We initialize result = 1.

2 is a common factor that appears in
two or more elements. We divide all
multiples by two and multiply result
with 2.
arr[] = {1, 1, 3, 2, 14}
result = 2

2 is again a common factor that appears 
in two or more elements. We divide all
multiples by two and multiply result
with 2.
arr[] = {1, 1, 3, 1, 7}
result = 4

Now there is no common factor that appears
in two or more array elements. We multiply
all modified array elements with result, we
get.
result = 4 * 1 * 1 * 3 * 1 * 7
 = 84

Below is the implementation of above algorithm. 
 

Output: 
 

420

Time Complexity: O(max * n), where n represents the size of the given array and m represents the maximum element present in the array.
Auxiliary Space: O(n), where n represents the size of the given array.