Least common multiple of two or more numbers.
This LCM calculator finds the least common multiple of two or more whole numbers. It breaks each number into prime factors, takes the highest power of each prime, and multiplies them together, showing every step. It also gives the greatest common factor for reference.
The LCM of the denominators is the lowest common denominator (LCD), which you need to add or subtract fractions.
Quick answer: the LCM is the smallest number that all your numbers divide into exactly. Write each number as prime factors, take the highest power of each prime that appears, and multiply. For 4 = 2² and 6 = 2 × 3, the LCM is 2² × 3 = 12.
How to Use the LCM Calculator
- Enter two or more non-zero whole numbers, separated by commas, such as 4, 6, 15.
- Read the least common multiple and the GCF for reference.
- Follow the prime factors in the steps.
Three Ways to Find the LCM
1. List the multiples (good for small numbers)
Multiples of 6: 6, 12, 18, 24, 30. Multiples of 8: 8, 16, 24, 32. The first one in both lists is 24.
2. Prime factorization (good for three or more numbers)
4 = 2², 6 = 2 × 3, 15 = 3 × 5. Take the highest power of each prime: 2², 3 and 5. LCM = 4 × 3 × 5 = 60.
3. Use the GCF (fastest for two large numbers)
LCM = (a × b) ÷ GCF(a, b)
For 48 and 180, the GCF is 12, so LCM = 48 × 180 ÷ 12 = 720. The GCF calculator finds the GCF with Euclid’s method.
LCM Examples
| Numbers | LCM |
|---|---|
| 4 and 6 | 12 |
| 6 and 8 | 24 |
| 12 and 18 | 36 |
| 4, 6 and 8 | 24 |
| 4, 6 and 15 | 60 |
| 48 and 180 | 720 |
Using the LCM to Add Fractions
To add 1/4 + 1/6, find the LCM of 4 and 6, which is 12. Rewrite both fractions over 12: 3/12 + 2/12 = 5/12.
Using 24 (4 × 6) would also work, but you would then have to simplify the answer. The LCM keeps the numbers as small as possible. The fraction calculator finds the lowest common denominator automatically.
Where the LCM Is Used
- Schedules that repeat: buses every 12 and 18 minutes leave together again after 36 minutes.
- Buying in packs: hot dogs in 10s and buns in 8s match up at 40 of each, which is 4 packs of hot dogs and 5 of buns.
- Gears and cycles: working out when two rotating parts line up again.
LCM Calculator FAQs
What is the LCM of two prime numbers?
Their product. The LCM of 5 and 7 is 35, because they share no factors.
Can the LCM be one of the numbers?
Yes, when the other numbers divide into it. The LCM of 4 and 12 is 12.
Is the LCM the same as the lowest common denominator?
The lowest common denominator is the LCM of the denominators of a set of fractions. It is the same calculation applied to the bottom numbers.
Why can’t I use zero?
Every number divides into 0, so a “least common multiple” with 0 is not useful. The calculator asks for non-zero numbers.
How we checked this page: every LCM in the table was checked by listing multiples and by prime factors, and matches the calculator.