MyMaths MyLife

Least Common Multiple (L.C.M):


Rules:

The smallest of the common multiples of two natural numbers (a and b) is called the least common multiple(LCM) of the numbers a and b.

The smallest of the common multiples of two or more natural numbers is called the least common multiple(LCM).

If two numbers are c0-prime, then their LCM is equal to their product.

Given two numbers, if the first number is a multiple of the second number, then their LCM is equal to the first number.

Relationship Between GCD and LCM:
If a and b are any two natural numbers and L and G are respectively their LCM and GCD, then a*b=L*G

Example:

LCM of 30,48

2 |30,48
_______
3 |15,24
_____
5,8

LCM of 30,48 = 2*3*5*8= 240

Factorial is defined for any positive integer. It is denoted by !. Thus “Factorial n” is written as n!. n! is defined as the product of all the integers from 1 to n.

Thus n! = 1.2.3.. ... (n-1),n.

Example 5! = 1*2*3*4*5 = 120

0! is defined to be equal to 1.
Therefore 0! = 1 and 1! = 1

n!=n*(n-1)!
eg: 10!=10*(10-1)!=10*(9)!