Permutation question

Question

LCM of 4! 5! 6!

Answer 1

LCM of 4! 5! 6!

 

6! = 6(5!) = 6(5)(4!)

 

The smallest thing all 3 divide into is

6! which is 720

Answer 2

720

 

 

 

Explanation:

 

How to find LCM:

 

 step 1: list multiples of the largest

 step 2: find the first multiple in the list that divides by the other numbers

 repeat steps 1-2 as needed.

 

 Ex.    LCM( 2,3,5)

  multiples of 5: 5,10,15,20,25,30,35,40,45,50,....

  30 divides by 2 and 3

 

  LCM(2,3,4,6)

   multiples of 6: 6,12,18,24,30,36,....

     12 divides by 2,3 and 4

 

Now back to this problem:

4!=24,            5!=120      and   6!=720

 LCM (24,120,720)

 

 starting by listing multiples of 720:  720x1=720 ,720x2=1440, 720x3 = 2160,....

 

 Find the first one of these that divides by 24 and 120...

 

720