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What is Lowest Common Multiple/Least Common Multiple/Smallest Common Multiple?

The smallest common multiple of two or more numbers is called the LCM (Lowest Common Multiple) or the smallest number that can be divided by the given two or more numbers.

LCM of two integers a and b is the smallest positive integer that is a multiple of both of a and of b. Since it is a multiple, it can be divided by a and b without a remainder

Generalized definition: The lowest common multiple of integers a1,a2,... an is the smallest positive integer that is a multiple of a1,a2,... an or the smallest positive integer that can be divided by a1,a2,... an widthout remainder.

### Facts About Multiples:

It can be used to find the lowest common denominator when adding or subtracting fractions.

If any of the given number is 0 (zero) then the LCM of the numbers is also 0 (zero).

LCM (Lowest Common Multiple) is also known by least common multiple or smallest common multiple.

### How to find LCM of the given numbers.

1. Find the prime factors of the given numbers.

2. Select all the factors which are common to at least two numbers once.

3. Select all the factors which are not common to at least two numbers.

4. Multiply all the selected factors. The result is the LCM of the given numbers.

### Example: Find LCM of 10, 15 and 18.

Prime factors of 10: 2 , 5

Prime factors of 15: 3 , 5

Prime factors of 18: 2 , 3 , 3

Factors which are common to at least two numbers: 2 , 3 , 5

Factors which are not common to at least two numbers: 3

LCM = 2 * 3 * 5 * 3 = 90