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What is a Factorial?  
A factorial is a function whose domain is the set of whole numbers.
⇒ Factorials are defined for whole numbers only.
Thus "k" would be equal to 1 both when "n" = 0 as well as when "n" = 1. 
Factorial Interpretation  
You will find factorials being used all throughout the topic permutations and combinations. It is a general idea which is also used in many other topics in mathematics. Knowing various ways in which the factorial may be interpreted would be useful in problem solving.
• Factorial of 0 (Zero)
0! = 1
Empty/Nullary ProductAn empty product, or nullary product, is the result of multiplying no numbers.Its numerical value is 1 (the multiplicative identity).
Two most frequent instances of empty product are:
• Factorial of a natural number
The factorial of a natural number "n" is the product of the all natural numbers less than or equal to "n".
⇒ Factorial "n" = 1 × 2 × 3 × ... × n.
Example
Factorial of 8 is the product of natural numbers starting with 1 and ending with 8.
⇒ 8! or ∠8 = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 • Factorial of 1 (One)
n! = 1 x 2 x 3 x 4 x ...x (n − 2) x (n − 1) x n. ⇒ 1! = 1
• Expanding factorials
This would be most useful for simplifications of problems involving factorial notations. 
Factorials » Arithmetic Operations  
• Multiplication
Product of two or more factorials is the product of their values.
• Division
The simplification process can be reduced by expanding the factorial notation.
• Addition
• Subtraction

LCM of Factorials  
LCM :: Explanation » Hide/Show
LCM is "Least Common Multiple".
Multiples
Multiples of a number are the successive products of the number and the natural numbers.
Common Multiples
Common multiples of two or more number are the multiples of the numbers which are common to all of them.
The common multiples of 4, 5, 8 are 40, 80, 120 .... Least Common Multiple
LCM of a set of numbers is the least of the common multiples of those numbers
In the above case LCM of 4, 5, 8 is 40 since 40 is the least of the common multiples. The multiples of the LCM will also be the common multiples of the given numbers.
Factor
A factor of a given number is that number which divides it completely.
A number is a factor of its MultipleSince a multiple is a product of the number and a natural number, the multiple of a number is always divisible by the number. Therefore we can say that a number is a factor of its multiple.Test for LCM!!
LCM of a set of numbers is divisible by all the numbers in the set.
If "x" is the LCM of "a, b and c", then "x" is divisible by each of "a, b and c". To test whether a certain number is the LCM of two or more given numbers, we use this test of divisibility.
The Highest of the given numbers may be the LCM
Since LCM should be divisible by all the given numbers whose LCM it is, it cannot be less than the highest of the given numbers. If at all one of the given numbers itself has a chance of being the LCM, it is the highest of the given numbers.
To test whether the highest of the given numbers is the LCM or not, divide it by the other numbers. If it is divisible by all of them completely then it is the LCM, otherwise not. Since LCM ultimately should be a multiple of all the given numbers, if the highest number is not the LCM, then one of its multiples would be. This understanding can be used to calculate LCM orally for smaller numbers. Example
• Where all the numbers are Factorials
Where all the given numbers are factorials, their LCM would be the highest of them
• Where all the numbers are not Factorials

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