Concept 5 of 6
LCM: The Lowest Common Multiple
Today's big idea
The lowest common multiple is the first number both counting sequences reach.
Lowest names the earliest meeting point, not the smaller of the two numbers.
How it works
👀 What's going on?
Two alarms are set, one repeating more often than the other. Sooner or later they go off at the very same moment, and the LCM tells you when.
💡 Here's the trick
Look at the timeline above. The LCM is the smallest number that every number in the set divides into. Because the largest number has to divide it, the LCM can never be smaller than that number.
🪄 How to do it
- 1.Break each number into primes, using the timeline above.
- 2.Collect every prime that appears in any of them.
- 3.Take each one at its highest power and multiply.
✍️ Try it
Find the LCM of 9 and 15. Then: find the LCM of 14 and 21.
9 is 3² and 15 is 3 × 5, so the highest powers give 3² × 5 = 45. 14 is 2 × 7 and 21 is 3 × 7, so the highest powers give 2 × 3 × 7 = 42.
⚠️ Watch out
You might be thinking the LCM is just the two numbers multiplied together. That only holds when they share no factor at all. For 9 and 15 the product is 135, but the LCM is only 45.
🌟 Why this matters
Buses that leave together, lights that blink together and gears that line up again all repeat after their LCM. It is also the shared bottom you need before adding two fractions.
Exam tip: For two numbers, HCF × LCM equals their product, which checks your answer in seconds.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find the LCM of 10 and 15.”
- 1
Prime factorise each
10 = 2 × 5. 15 = 3 × 5. ⏱️
- 2
Pick EVERY prime that appears
2, 3 and 5.
- 3
Multiply them once each
2 × 3 × 5 = 30
- 4
LCM ✓
LCM(10, 15) = 30
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Skip-count both numbers. The FIRST multiple in both rows is the LCM.
LCM OF 4 & 10 · ROUND 1 OF 3
Quick check
✅ VERIFICATION
What is the LCM of 12 and 16?
⚡ Finish the activity above first to answer.
Keep going!
Up next: HCF & LCM Word Problems
Look for the signal-word, then pick your tool.