The LCM of 4 and 5 is 20. Since 4 and 5 are coprime (they share no common factors other than 1), their LCM is simply their product: 4 × 5 = 20. This guide covers everything you need to know about finding the least common multiple of 4 and 5: three proven methods, custom site-themed SVG Venn and gear synchronization diagrams, step-by-step examples, the relationship between LCM and GCD, real-world applications, and answers to frequently asked questions.
The LCM of 4 and 5 is 20. The Least Common Multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers without leaving a remainder.
For 4 and 5, the LCM is 20 because:
Visualization of the first 10 multiples of 4 and 5 on a number line using the brand color palette. The first point of intersection is 20.
There are three standard methods to find the LCM of 4 and 5. Each method gives the exact same result: 20.
Since 4 and 5 share no common factors, simply multiply them: 4 × 5 = 20.
Break 4 and 5 into prime factors, take the highest power of each prime, and multiply.
List the multiples of 4 and 5 until you find the smallest number they share — which is 20.
The prime factorization method works for any set of numbers and confirms why the coprime shortcut works.
Designed with website theme colors: Because 4 and 5 are coprime, their intersection contains no common prime factors (GCD = 1). The LCM is directly the product of all factors: 2² × 5 = 20.
| Number | Prime Factorization | 2 | 5 | Highest Power |
|---|---|---|---|---|
| 4 | 22 | 22 | — | — |
| 5 | 51 | — | 51 | — |
| LCM | 22 × 51 | 22 | 51 | 4 × 5 = 20 |
In the division method, we divide 4 and 5 by prime factors until no further division is possible.
| Prime Factor | 4 | 5 |
|---|---|---|
| 2 | 2 | 5 |
| 2 | 1 | 5 |
| 5 | 1 | 1 |
LCM(4, 5) = 2 × 2 × 5 = 20
List the multiples of 4 and 5 until you find the smallest common multiple.
| Number | Multiples | First Common |
|---|---|---|
| 4 | 4, 8, 12, 16, 20, 24, 28, … | 20 |
| 5 | 5, 10, 15, 20, 25, 30, … |
The LCM and GCD (Greatest Common Divisor) of 4 and 5 are different values that serve complementary purposes in mathematics. Since 4 and 5 are coprime, their GCD is 1.
| Aspect | LCM of 4 and 5 | GCD of 4 and 5 |
|---|---|---|
| Definition | Smallest number divisible by both 4 and 5 | Largest number that divides both 4 and 5 |
| Value | 20 | 1 |
| Relationship | LCM(4, 5) × GCD(4, 5) = 20 × 1 = 20 = 4 × 5 ✓ | |
| Size | Always ≥ 5 (the largest input) | Always ≤ 4 (the smallest input) |
| Primary Use | Adding fractions, scheduling | Simplifying fractions, grouping |
The LCM of 4 and 5 isn't just a mathematical concept — it appears in many practical situations where repeating events need to align.
Rendered with site brand colors: A 4-tooth gear completes 5 full revolutions, while a 5-tooth gear completes 4 full revolutions to re-synchronize at 20 units.
| Field | Problem | LCM Role | Example |
|---|---|---|---|
| Mathematics | Adding fractions | Find common denominator | 1/4 + 1/5 = 5/20 + 4/20 = 9/20 |
| Scheduling | Repeating events | When events align | Bus every 4 min & 5 min → every 20 min |
| Mechanics | Gear rotation | Re-alignment point | 4-tooth & 5-tooth gears → 20 turns |
| Commerce | Package sizes | Equal quantities | 4-pack & 5-pack → buy 20 of each |
| Music | Rhythm pattern | Pattern re-sync | 4/4 & 5/4 time → 20 beats |
To add 1/4 + 1/5, find the LCD (Least Common Denominator), which is LCM(4, 5) = 20.
If one bus leaves every 4 minutes and another every 5 minutes, they will depart together every LCM(4, 5) = 20 minutes.
Three fully solved examples using different methods.
| Step | Action | Result |
|---|---|---|
| 1 | Check GCD of 4 and 5 | GCD(4, 5) = 1 (coprime) |
| 2 | Apply coprime rule: LCM = a × b | LCM = 4 × 5 = 20 |
| ✓ | Verify | 20 ÷ 4 = 5 ✓; 20 ÷ 5 = 4 ✓ |
Find LCM(4, 5) using GCD(4, 5) = 1.
Find the first common multiple of 4 and 5.
Even experienced students make these errors. Watch out for them.
| ❌ Mistake | Why it's wrong | ✅ Correct approach |
|---|---|---|
| Saying the LCM is 40 | 40 is a common multiple, but not the least common multiple | The LCM of 4 and 5 is 20 |
| Confusing LCM with GCD | GCD(4, 5) = 1, but LCM(4, 5) = 20 | Remember: LCM ≥ max(4, 5); GCD ≤ min(4, 5) |
| Assuming LCM = a × b always | Only works when numbers are coprime (GCD = 1). For 12 and 18, this fails | Always check GCD first — it works here because GCD(4, 5) = 1 |
| Using the division method incorrectly | Trying to divide by a common factor when none exists | Since 4 and 5 have no common prime factors, just multiply them |
Quick answers to the most common questions about the LCM of 4 and 5.
The LCM of 4 and 5 is 20. It is the smallest positive integer that is divisible by both 4 and 5. Since 4 and 5 are coprime, their LCM equals their product: 4 × 5 = 20.
Since 4 and 5 are coprime (GCD = 1), the fastest way is: LCM = 4 × 5 = 20. You can also use prime factorization (2² × 5 = 20), the division method, or listing multiples.
The LCM of 4, 5, and 10 is 20. Since 20 is already a multiple of 4, 5, and 10, the LCM remains 20.
No. While 40 is a common multiple of 4 and 5, it is not the least common multiple. The LCM of 4 and 5 is 20. 40 is simply the second common multiple.
The GCD (Greatest Common Divisor) of 4 and 5 is 1. Since they share no common factors other than 1, 4 and 5 are called coprime (or relatively prime).
For any two numbers: LCM(a, b) × GCD(a, b) = a × b. For 4 and 5: LCM(4, 5) × GCD(4, 5) = 20 × 1 = 20 = 4 × 5 ✓
LCM(4, 5) = 20 is used when adding fractions with denominators 4 and 5, when scheduling events that repeat every 4 and 5 minutes, and when finding when two gears with 4 and 5 teeth will realign.
Yes. Two numbers are coprime if their only common factor is 1. Since GCD(4, 5) = 1, they are coprime. This is why LCM(4, 5) = 4 × 5 = 20.
Key terms related to the LCM of 4 and 5.