# Arithmetic/Lowest Common Multiple

To find the Lowest Common Multiple (LCM) of several numbers, we first express each number as a product of its prime factors.

For example, if we wish to find the LCM of 60, 12 and 102 we write

The product of the highest power of each different factor appearing is the LCM.

For example in this case, . You can see that 1020 is a multiple of 12, 60 and 102 ... the lowest common multiple of all three numbers.

Another example: What is the LCM of 36, 45, and 27?

Solution: Factorise each of the numbers

The product of the highest power of each different factor appearing is the LCM, i.e.;

#### Properties of the LCM[edit]

If the LCM of the numbers is found and 1 is subtracted from the LCM then the remainder when divided by each of the numbers whose LCM is found would have a remainder that is 1 less than the divisor. For example if the LCM of 2 numbers 10 and 9 is 90. Then 90-1=89 and 89 divided by 10 leaves a remainder of 9 and the same number divided by 9 leaves a remainder of 8.