Key takeaways
- LCM(a, b) = (a × b) ÷ HCF(a, b).
- The LCM is always the smallest shared multiple, never smaller than either number.
- Find the HCF first — skipping it just gives a × b, a common multiple but not the lowest one.
- If two numbers share no common factor, their LCM is simply their product.
In this guide
What is the LCM?
LCM stands for Lowest Common Multiple. It's the smallest number that both of two given numbers can divide into with no remainder.
Why does the LCM matter?
Whenever two repeating things need to line up — bus schedules, flashing lights, or adding fractions with different denominators — the LCM tells you exactly when or where that happens.
Bus A (every 8 minutes) and Bus B (every 12 minutes), leaving together now, will next leave together in exactly LCM(8, 12) = 24 minutes.
The formula
| Symbol | What it means | Example |
|---|---|---|
| LCM(a, b) | The lowest common multiple | 24 |
| a | The first number | 8 |
| b | The second number | 12 |
How to find the LCM step by step
- 1Find the HCF (greatest common divisor) of your two numbers — see the HCF calculator if you need to find it first.
- 2Multiply the two original numbers together.
- 3Divide that product by the HCF you found in Step 1.
- 4The result is the LCM.
Try the calculator below with your own two numbers to see the full working.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Confusing LCM with HCF. LCM is the smallest shared multiple (bigger than or equal to both numbers); HCF is the largest shared factor (smaller than or equal to both numbers).
- Assuming the LCM is always a × b. That's only true when a and b share no common factor besides 1.
- Listing multiples forever. For big numbers, the HCF method is much faster than listing every multiple by hand.
Tips and tricks
- Listing multiples works too for small numbers: write out the multiples of each and spot the first one they share.
- Check your answer by dividing the LCM by both original numbers — both results should be whole numbers.
- Finding a common denominator when you add fractions is really just finding the LCM of the two denominators.
Where you'll use it in real life
- Scheduling: working out when two repeating events, like buses or shifts, line up again.
- Math class: finding a common denominator to add or compare fractions.
- Shopping: planning stock orders that come in different pack sizes.
- Music: understanding when two repeating rhythms or beats sync back up.
Quick summary
To find the LCM of two numbers, find their HCF first, multiply the two numbers together, then divide by that HCF. The result is the smallest number both original numbers divide into evenly. Try the calculator above with your own two numbers.
Worked example
Bus A leaves the station every 8 minutes and Bus B leaves every 12 minutes. If they both just left together, how many minutes until they leave together again?
- 01LCM = (a × b) ÷ HCF(a, b)
- 02HCF(8, 12) = 4
- 03LCM = (8 × 12) ÷ 4
- 04LCM = 96 ÷ 4
- 05LCM = 24
These numbers are pre-filled in the calculator above.
Frequently asked questions
What is the LCM used for in real life?
It's used to find a common denominator when adding or comparing fractions, and to figure out when two repeating events, like schedules or deliveries, will line up again.
How do I find the LCM without the HCF formula?
List the multiples of each number until you find the smallest one they share. For example, multiples of 8 are 8, 16, 24, 32… and multiples of 12 are 12, 24, 36… so the LCM is 24.
What is the LCM of two numbers that don't share a common factor?
It's simply their product. For example, the LCM of 5 and 9 is 45, since HCF(5, 9) = 1 and 5 × 9 ÷ 1 = 45.
Is the LCM ever smaller than one of the original numbers?
No. The LCM is always a multiple of both numbers, so it's always greater than or equal to the larger of the two numbers.
