Lowest common multiple
What is the lowest common multiple?
Section titled “What is the lowest common multiple?”The LCM (lowest common multiple) of numbers is the smallest multiple that is common to both/all numbers.
In other words, it’s the smallest number that both/all numbers go into.
For example, the LCM of
Finding the lowest common multiple
Section titled “Finding the lowest common multiple”To find the lowest common multiple, you need to be familiar with prime factorisation.
Here are the steps:
- Find the prime factorisation of each number.
- For each different prime factor, take the highest power of that factor that appears in any of the numbers.
- Multiply these together to get the LCM.
Example: Find the LCM of
Section titled “Example: Find the LCM of and .”- Find the prime factorisation of each number:
- For each different prime factor, take the highest power:
- For
, the highest power is (from ) - For
, the highest power is (from )
- For
- Multiply these together:
Answer:
Example: Find the LCM of
Section titled “Example: Find the LCM of , and .”- Find the prime factorisation of each number:
- For each different prime factor, take the highest power:
- For
, the highest power is (from all three numbers) - For
, the highest power is (from ) - For
, the highest power is (from ) - For
, the highest power is (from )
- For
- Multiply these together:
Answer: