Multiples and common multiples
A multiple of a number is the result of multiplying it by 1, 2, 3, and so on. The multiples of 4 are 4, 8, 12, 16, 20… A common multiple of two numbers appears in both lists, for example 12 is a common multiple of 4 and 6.
Key idea / Key idea
The Lowest Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both. It is never smaller than the larger of the two numbers.
Finding the LCM by listing
List the multiples of each number and pick the smallest one they share. Writing several multiples of the larger number first and checking which one the smaller number also divides is often the quickest route.
- Multiples of 4: 4, 8, 12, 16, 20, 24…
- Multiples of 6: 6, 12, 18, 24…
- The LCM of 4 and 6 is 12.
Finding the LCM by prime factors
Write each number as prime factors, then multiply the highest power of every prime that appears.
Worked example / Worked example
Find the LCM of 8 and 12.
8 = 23 and 12 = 22 × 3.
Take the highest powers: 23 × 3 = 8 × 3 = 24. So LCM = 24.
Remember / Remember
- For the LCM take the highest power of each prime; for the HCF take the lowest.
- The LCM is a multiple of both numbers.
- LCM is useful for events that repeat, like buses arriving together.