The LCM of 15 and 25 is 75. Both numbers share a common prime factor of 5, so their LCM is smaller than their product. This guide walks through everything — three methods, visual Venn diagrams, the GCD relationship, worked examples, applications, and FAQs.
The LCM of 15 and 25 is 75. The Least Common Multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers without leaving a remainder.
For 15 and 25, the LCM is 75 because:
Visualization of the first 10 multiples of 15 and 25. The first common multiple is 75.
Prime factors combine visually: the shared factor 5 forms the GCD (5), while multiplying all factors in the union (3 × 5 × 5) gives the LCM (75).
There are three standard methods to find the LCM of 15 and 25. Each one gives the same result: 75.
List the multiples of 15 and 25 and find the smallest number they share.
Break 15 and 25 into prime factors, take the highest power of each prime, and multiply.
Divide 15 and 25 by common prime factors until no further division is possible.
Prime factorization is the most reliable method — it works for any set of numbers.
| Number | Prime Factorization | 3 | 5 | Highest Power |
|---|---|---|---|---|
| 15 | 3 × 5 | 31 | 51 | — |
| 25 | 52 | — | 52 | — |
| LCM | 31 × 52 | 31 | 52 | 3 × 25 = 75 |
In the ladder method, we divide both numbers by common primes until no prime divides at least two numbers.
| Prime Factor | 15 | 25 |
|---|---|---|
| 5 | 3 | 5 |
| 3 | 1 | 5 |
| 5 | 1 | 1 |
LCM(15, 25) = 5 × 3 × 5 = 75
List the multiples of 15 and 25 until you find the smallest common multiple.
| Number | Multiples | First Common |
|---|---|---|
| 15 | 15, 30, 45, 60, 75, 90, … | 75 |
| 25 | 25, 50, 75, 100, 125, 150, … |
The LCM and GCD (Greatest Common Divisor) of 15 and 25 are different values that serve complementary purposes in mathematics.
| Aspect | LCM of 15 and 25 | GCD of 15 and 25 |
|---|---|---|
| Definition | Smallest number divisible by both 15 and 25 | Largest number that divides both 15 and 25 |
| Value | 75 | 5 |
| Relationship | LCM(15, 25) × GCD(15, 25) = 75 × 5 = 375 = 15 × 25 ✓ | |
| Size | Always ≥ 25 (the largest input) | Always ≤ 15 (the smallest input) |
| Primary Use | Adding fractions, scheduling | Simplifying fractions, grouping |
The LCM of 15 and 25 appears in many practical situations where repeating events need to align.
| Field | Problem | LCM Role | Example |
|---|---|---|---|
| Mathematics | Adding fractions | Find common denominator | 1/15 + 1/25 = 5/75 + 3/75 = 8/75 |
| Scheduling | Repeating events | When events align | Bus every 15 min & 25 min → every 75 min |
| Mechanics | Gear rotation | Re-alignment point | 15-tooth & 25-tooth gears → realign after 75 turns |
| Commerce | Package sizes | Equal quantities | 15-pack & 25-pack → buy 75 of each |
| Music | Rhythm pattern | Pattern re-sync | 15/8 & 25/8 time → realign every 75 beats |
To add 1/15 + 1/25, find the LCD (Least Common Denominator), which is LCM(15, 25) = 75.
If one bus leaves every 15 minutes and another every 25 minutes, they will depart together every LCM(15, 25) = 75 minutes.
Three fully solved examples using different methods.
| Step | Action | Result |
|---|---|---|
| 1 | Prime factorize 15 and 25 | 15 = 3 × 5; 25 = 5² |
| 2 | Take highest powers | 3¹, 5² |
| 3 | Multiply | 3 × 25 = 75 |
| ✓ | Verify | 75 ÷ 15 = 5 ✓; 75 ÷ 25 = 3 ✓ |
Find LCM(15, 25) using GCD(15, 25) = 5.
Find the first common multiple of 15 and 25.
Here are LCM values for pairs that commonly appear alongside LCM(15, 25).
Here are the most common errors students make on this pair — and how to avoid them.
| ❌ Mistake | Why it's wrong | ✅ Correct approach |
|---|---|---|
| Saying the LCM is 375 | 375 is the product 15 × 25, but not the least common multiple | The LCM of 15 and 25 is 75 |
| Multiplying 15 × 25 = 375 | Only works when numbers are coprime (GCD = 1). GCD(15, 25) = 5 | Use LCM = (15 × 25) ÷ GCD = 375 ÷ 5 = 75 |
| Taking 5¹ instead of 5² | 25 has 5², and the highest power wins | Use 5² = 25 for the prime 5 |
| Forgetting the prime 3 | 3 appears in 15 but not in 25 — but the LCM still includes it | Include every distinct prime that appears: 3 × 5² = 75 |
Quick answers to the most common questions about the LCM of 15 and 25.
The LCM of 15 and 25 is 75. It is the smallest positive integer that is divisible by both 15 and 25.
Use prime factorization: 15 = 3 × 5 and 25 = 5². Take the highest power of each prime: 3 × 5² = 3 × 25 = 75. You can also use the division method, list multiples until you reach 75, or use the GCD method: (15 × 25) ÷ 5 = 75.
The GCD (Greatest Common Divisor) of 15 and 25 is 5. The common factors of 15 and 25 are 1 and 5, and 5 is the largest.
For any two numbers: LCM(a, b) × GCD(a, b) = a × b. For 15 and 25: LCM(15, 25) × GCD(15, 25) = 75 × 5 = 375 = 15 × 25 ✓
No. While 150 is a common multiple of 15 and 25, it is not the least common multiple. The LCM of 15 and 25 is 75. 150 is simply the second common multiple.
The LCM of 15, 25, and 50 is 150. Prime factorization: 15 = 3 × 5, 25 = 5², 50 = 2 × 5². Highest powers: 2 × 3 × 5² = 150.
The LCM of 15 and 25 is 75, which is an integer. The formula for LCM of fractions is different: LCM(a₁/b₁, a₂/b₂) = LCM(numerators) ÷ GCD(denominators).
LCM(15, 25) = 75 is used when adding fractions with denominators 15 and 25, when scheduling events that repeat every 15 and 25 minutes, and when finding when two gears with 15 and 25 teeth will realign.
Key terms related to the LCM of 15 and 25.