Hello, young mathematician! 👋 Today we're learning about two very useful ideas in maths — LCM and HCF. We use simple language, Venn diagrams, fun stories, and clear steps. Click any topic below to jump straight to it:
Let's start by understanding what LCM and HCF really mean.
Take the multiples of two numbers. The smallest number that appears in both lists is the LCM.
Take the factors of two numbers. The biggest number that appears in both lists is the HCF.
Imagine two friends, Anna and Ben, who love running around a track. Anna finishes a lap every 4 minutes, and Ben finishes every 6 minutes. They start together.
Anna is at the start line every 4 minutes: 4, 8, 12, 16, 20, 24, …
Ben is at the start line every 6 minutes: 6, 12, 18, 24, 30, …
When do they both meet at the start line together again? The first time is after 12 minutes! That's the LCM(4, 6) = 12.
Suppose you have 12 candies 🍬 and 18 chocolates 🍭. You want to make gift bags with the same number of each, using up all the candies and chocolates.
What's the biggest number of gift bags you can make? Both 12 and 18 can be divided by 6 evenly. So 6 gift bags! That's the HCF(12, 18) = 6.
Did you know you can see both HCF and LCM inside a single simple picture? Let's look at the numbers 12 and 18.
Prime factors: 12 = 2 × 2 × 3, 18 = 2 × 3 × 3. The middle overlap gives the HCF. Multiplying all parts across the circles gives the LCM!
2 × 3 = 6.2 × (2 × 3) × 3 = 36. Easy peasy!The easiest way for Class 5 is to list the multiples. Let's find LCM(4, 6).
Once you're comfortable with listing, you can try the division method — also called the ladder method. You just divide the numbers by small primes (2, 3, 5) until you can't divide anymore.
For HCF, we list the factors (numbers that divide evenly). Let's find HCF(12, 18).
With the ladder method, the HCF is just the product of the divisors on the left (without the last row).
This is the most important thing to remember. Let's compare them side by side.
| Point | LCM (Least Common Multiple) | HCF (Highest Common Factor) |
|---|---|---|
| What is it? | Smallest number both numbers jump to | Biggest number that divides both numbers |
| Uses | Multiples (jumps forward: 4, 8, 12...) | Factors (breaks down: 1, 2, 4...) |
| Size | Bigger than or equal to both numbers | Smaller than or equal to both numbers |
| Example | LCM(4, 6) = 12 | HCF(4, 6) = 2 |
| When to use | When things repeat or align (clocks, laps) | When you share or divide equally (candies, tiles) |
Here are the answers for some pairs you'll see often in Class 5. Try to remember these!
| Pair | LCM | HCF |
|---|---|---|
| 2, 3 | 6 | 1 |
| 3, 4 | 12 | 1 |
| 4, 6 | 12 | 2 |
| 6, 8 | 24 | 2 |
| 6, 9 | 18 | 3 |
| 8, 12 | 24 | 4 |
| 9, 12 | 36 | 3 |
| 10, 15 | 30 | 5 |
| 12, 18 | 36 | 6 |
| 15, 20 | 60 | 5 |
Try these in your notebook. Check your answers below!
| Question | Answer |
|---|---|
| LCM(3, 5) | 15 |
| LCM(6, 8) | 24 |
| HCF(6, 9) | 3 |
| HCF(10, 20) | 10 |
| LCM(5, 10) | 10 |
| HCF(8, 12) | 4 |
Keep these tips in mind whenever you solve LCM or HCF problems:
You've just learned about two of the most important ideas in maths — LCM and HCF. Whenever you need to find them, remember:
LCM means Least Common Multiple. It is the smallest number that appears in the multiples of both given numbers. For example, LCM(4, 6) = 12.
HCF means Highest Common Factor. It is the biggest number that divides both given numbers evenly. For example, HCF(12, 18) = 6.
For Class 5, the easiest way is to list the multiples of each number and circle the first number that appears in both lists. For example, multiples of 4 are 4, 8, 12, …; multiples of 6 are 6, 12, 18, … — so the LCM is 12.
List all the factors of each number, then circle the biggest factor that appears in both lists. For example, factors of 12 are 1, 2, 3, 4, 6, 12; factors of 18 are 1, 2, 3, 6, 9, 18 — so the HCF is 6.
LCM and HCF help us solve many real-life problems — like figuring out when two events will happen together (LCM), or how to share things equally among friends (HCF). They're also the foundation for fractions you'll learn in higher classes.
Yes! The ladder method (also called the division method) is a fast shortcut. You divide both numbers by small primes until you can't anymore. For LCM, multiply all numbers in the ladder; for HCF, multiply only the divisors on the left.