LCM Calculator
Find the Least Common Multiple (LCM) of two or more numbers. See step-by-step prime factorization and the relationship between LCM and GCF.
LCM(a,b) = |a × b| / GCF(a,b)Results
LCM
36
Input Mode
Enter Numbers
Results
Least Common Multiple
36
Greatest Common Factor
6
Step-by-Step Solution
Prime factorizations:
12 = 2^2 × 3
18 = 2 × 3^2
LCM = product of highest powers of all primes:
LCM = 2^2 × 3^2 = 36
GCF = product of lowest powers of common primes:
GCF = 2 × 3 = 6
Relationship: LCM × GCF = Product of numbers
36 × 6 = 216
12 × 18 = 216
Prime Factorizations
12
= 2^2 × 3
18
= 2 × 3^2
Common LCM Examples
| Numbers | LCM | GCF | Use Case |
|---|---|---|---|
| 2, 3 | 6 | 1 | Every 2 and 3 hours |
| 4, 6 | 12 | 2 | Fractions 1/4 + 1/6 |
| 5, 7 | 35 | 1 | Coprime numbers |
| 12, 15 | 60 | 3 | Minutes in schedules |
| 8, 12 | 24 | 4 | Hours in a day |
| 3, 4, 5 | 60 | 1 | Three-way scheduling |
| 2, 3, 4 | 12 | 1 | Months/seasons |
| 6, 8, 12 | 24 | 2 | Work shifts |
Methods to Find LCM
1. Prime Factorization Method
Find prime factors of each number, take the highest power of each prime.
LCM(12, 18) = LCM(2² × 3, 2 × 3²) = 2² × 3² = 36
2. Formula Method
Use the relationship with GCF: LCM(a,b) = |a × b| / GCF(a,b)
LCM(12, 18) = (12 × 18) / GCF(12, 18) = 216 / 6 = 36
3. Listing Multiples Method
List multiples of each number until finding the smallest common one.
12: 12, 24, 36, 48... | 18: 18, 36, 54...
Results
LCM
36
?How to Find the LCM
The Least Common Multiple (LCM) is the smallest positive number that is divisible by all given numbers. To find the LCM: list prime factors of each number, take each prime factor at its highest power, and multiply together. For example, LCM(4, 6) = 12, because 12 is the smallest number that both 4 and 6 divide into evenly.
What is the Least Common Multiple?
The Least Common Multiple (LCM), also called Lowest Common Multiple, is the smallest positive integer that is divisible by two or more given integers. It is essential for adding and subtracting fractions, synchronizing periodic events, and solving problems involving repeating cycles or schedules.
Key Facts About LCM
- LCM (Least Common Multiple) is the smallest positive number divisible by all given numbers
- LCM formula using GCF: LCM(a,b) = |a x b| / GCF(a,b)
- To find LCM by prime factorization: multiply each prime factor at its highest power
- LCM is used for adding fractions with different denominators
- LCM helps find when repeating events will coincide (scheduling problems)
- For coprime numbers (GCF=1), LCM equals their product
- LCM of any number and itself is that number
- LCM is always greater than or equal to the largest of the input numbers
Quick Answer
The Least Common Multiple (LCM) is the smallest positive number that is divisible by all given numbers. To find the LCM: list prime factors of each number, take each prime factor at its highest power, and multiply together. For example, LCM(4, 6) = 12, because 12 is the smallest number that both 4 and 6 divide into evenly.
Frequently Asked Questions
The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by all of those numbers. For example, LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6.
There are several methods: 1) List multiples until you find a common one, 2) Use prime factorization and take the highest power of each prime, 3) Use the formula LCM(a,b) = |a×b| / GCF(a,b). The prime factorization method is most efficient for larger numbers.
For any two numbers a and b: LCM(a,b) × GCF(a,b) = a × b. This relationship is useful for finding one when you know the other. Note: this formula only applies directly to two numbers.
LCM is used when finding common schedules (e.g., two buses running every 15 and 20 minutes meet every 60 minutes), adding fractions with different denominators, synchronizing repeating events, and solving problems about cycles.
When two numbers are coprime (no common factors except 1), their LCM equals their product. For example, LCM(7, 9) = 63 = 7 × 9, since 7 and 9 share no common prime factors.
Yes! LCM can be found for any set of numbers using prime factorization. Take the highest power of each prime that appears in any factorization. Alternatively, calculate LCM(a,b), then LCM(result, c), and so on.
Last updated: 2025-01-15
Results
LCM
36