Calculate the Least Common Multiple (LCM) of two or more numbers. Shows prime factorisation and step-by-step solution.
The least common multiple (LCM) is the smallest number that two or more numbers all divide into. To find it, list the multiples of each number and pick the smallest they share, or multiply the highest power of each prime factor. For example, the LCM of 4 and 6 is 12. LCM is also called the lowest common multiple. This calculator shows every step.
The least common multiple is the smallest positive integer that two or more numbers all divide into exactly. It is used mainly to add fractions and to find when repeating events line up. LCM and lowest common multiple mean the same thing.
There are three reliable ways to find the LCM. This calculator uses all three so you can see the full working.
You can also find the LCM with the Euclidean algorithm. It is normally used to find the GCF first — by repeatedly dividing and taking remainders — and once the GCF is known, the least common multiple follows directly from LCM = (a × b) ÷ GCF. This is why the GCF formula and the Euclidean algorithm are closely linked.
These tables show how LCM relates to GCF and how the three methods compare.
| Feature | LCM (Least Common Multiple) | GCF (Greatest Common Factor) |
|---|---|---|
| Meaning | Smallest multiple shared by the numbers | Largest factor shared by the numbers |
| Result size | Never smaller than the largest number | Never larger than the smallest number |
| Main use | Adding fractions, repeating events | Simplifying fractions, sharing evenly |
| Example (12 & 18) | 36 | 6 |
| Method | Best For | Notes |
|---|---|---|
| Listing multiples | Small numbers | Simple but slow for large values |
| Prime factorization | Medium numbers | Shows shared structure clearly |
| GCF formula | Any size | Fastest once the GCF is known |
| Numbers | LCM | GCF |
|---|---|---|
| 4 and 6 | 12 | 2 |
| 8 and 12 | 24 | 4 |
| 5 and 7 | 35 | 1 (coprime) |
| 9 and 12 | 36 | 3 |
The lowest common denominator (LCD) is the least common multiple of the denominators of two or more fractions. To add or subtract fractions with different denominators, you rewrite them over the LCD. For example, adding 1/4 and 1/6 uses LCD = LCM(4, 6) = 12, giving 3/12 + 2/12 = 5/12. This is one of the most common everyday uses of the LCM.
| LCM | LCD |
|---|---|
| Applies to whole numbers | Applies to fractions |
| Smallest shared multiple | Smallest shared denominator |
| Used to compare or combine multiples | Used to add or subtract fractions |
| Same calculation method | Is the LCM of the denominators |
smallest multiple shared by all numbersmultiply the highest power of each primeLCM(a,b) = a × b ÷ GCF(a,b)LCM(a,b,c) = LCM(LCM(a,b), c)LCM = a × bLCD = LCM of the denominators
1) 6 2) 8 3) 10 4) 18 5) 21
1) 72 2) 15 = 3×5, 20 = 2²×5 → 2²×3×5 = 60 3) GCF(24,36)=12, LCM = 24×36÷12 = 72 4) LCM(6,8) = 24 5) LCM(8,12) = 24 seconds
What is LCM?
LCM stands for least common multiple. It is the smallest positive number that two or more numbers all divide into exactly. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number both 4 and 6 divide into. It is widely used to add fractions and schedule repeating events.
What does LCM stand for?
LCM stands for least common multiple, sometimes called the lowest common multiple. Both names describe the same value: the smallest number that is a multiple of every number in a set. It is the counterpart of the greatest common factor (GCF).
What is the least common multiple?
The least common multiple of two or more integers is the smallest positive integer that each divides into without a remainder. For 3 and 4, the LCM is 12 — the smallest number in all their multiplication tables.
How do you find the LCM?
List the multiples of each number and choose the smallest they share, or use prime factorization and multiply the highest power of each prime. The fastest method is the GCF formula: LCM(a, b) = a × b ÷ GCF(a, b). This calculator shows all three methods with steps.
How do you calculate the LCM?
Pick a method and follow its rule. For prime factorization, factor each number and multiply the highest power of every prime. For the GCF formula, multiply the numbers and divide by their GCF. Enter your numbers above to see the steps.
How do you find the LCM of three numbers?
Find the LCM of the first two numbers, then find the LCM of that result with the third. For example, for 12, 18 and 24: LCM(12, 18) = 36, then LCM(36, 24) = 72. This calculator accepts several numbers separated by commas and does this automatically.
Can the LCM be 1?
The LCM is 1 only when every number in the set is 1. For any set containing a number greater than 1, the LCM is at least as large as the biggest number, so in practice it is rarely 1.
Is LCM the same as lowest common multiple?
Yes. Least common multiple (LCM) and lowest common multiple are two names for exactly the same thing — the smallest number that two or more numbers all divide into. Different textbooks and regions simply prefer different wording.
What is the difference between LCM and GCF?
The LCM is the smallest multiple shared by the numbers, while the greatest common factor (GCF) is the largest factor shared by them. LCM(4, 6) = 12, but GCF(4, 6) = 2. They are linked by the rule LCM(a, b) × GCF(a, b) = a × b.
Why is the LCM important?
The LCM provides the lowest common denominator for adding fractions and solves timing problems where events repeat at different intervals. It also appears in ratios, algebra and number theory, making it a core school skill.
How is the LCM used with fractions?
To add or subtract fractions with different denominators, rewrite them over a common denominator. The lowest common denominator (LCD) is the LCM of the denominators — for example, adding 1/4 and 1/6 uses LCM(4, 6) = 12, giving 5/12.
How do you find the LCM using prime factorization?
Factor each number into primes, then take the highest power of every prime that appears in any number and multiply them together. For 12 = 2² × 3 and 18 = 2 × 3², the highest powers are 2² and 3², so the LCM is 2² × 3² = 36.
How do you find the LCM using the GCF?
Use the formula LCM(a, b) = a × b ÷ GCF(a, b). First find the greatest common factor, then multiply the two numbers and divide by it. For 12 and 18, the GCF is 6, so the LCM is 12 × 18 ÷ 6 = 36. This is often the quickest method.
Is the LCD the same as the LCM?
The lowest common denominator (LCD) is the least common multiple (LCM) of the denominators of a set of fractions. So the LCD is a specific use of the LCM: you calculate it in exactly the same way, but apply it to the bottom numbers of fractions. For 1/4 and 1/6, the LCD is LCM(4, 6) = 12.