LCM Calculator
Enter two or more whole numbers below to instantly find their least common multiple (LCM), with the method shown.
What Is the LCM?
The least common multiple (LCM) of two or more numbers is the smallest positive number that all of them divide into evenly. It's the mirror image of the greatest common factor (GCF), which finds the largest number that divides evenly into a set of numbers instead.
How to Find the LCM, Step by Step
- Find the greatest common factor (GCF) of the numbers.
- Multiply the numbers together, then divide by the GCF: LCM(a, b) = (a × b) ÷ GCF(a, b).
- The result is the smallest number that every original number divides into evenly.
Worked example
Find the LCM of 12 and 18.
GCF(12, 18) = 6
LCM(12, 18) = (12 × 18) ÷ 6 = 216 ÷ 6 = 36
Check: 36 ÷ 12 = 3 and 36 ÷ 18 = 2 — both divide evenly, and 36 is the smallest number for which that's true.
Keep going
- LCM comes from the prime factors of both numbers; the factors table shows those for every number up to 100. Factors of every number
- LCM and GCF come from the same prime factorization; the GCF calculator finds the largest shared factor instead of the smallest shared multiple. GCF Calculator
- Finding a common denominator for fractions is just the LCM of the denominators; the LCD calculator applies that same method directly to fractions. LCD Calculator
Frequently Asked Questions
What is the LCM of two numbers?
The least common multiple (LCM) of two or more numbers is the smallest positive number that is a multiple of all of them. For example, the LCM of 4 and 6 is 12, since 12 is the smallest number both 4 and 6 divide into evenly.
How do you find the LCM without a calculator?
List the multiples of each number until you find the smallest one they share, or use the formula LCM(a, b) = (a × b) ÷ GCF(a, b). The second method is faster for larger numbers since it only requires finding the greatest common factor first.
What is the LCM used for?
LCM is most often used to add or subtract fractions with different denominators — you need a common denominator, and using the least common one keeps the numbers as small as possible. It also comes up in scheduling problems (when do two repeating events line up again) and in simplifying ratios.
What's the difference between LCM and GCF?
GCF (greatest common factor) is the largest number that divides evenly into a set of numbers. LCM (least common multiple) is the smallest number that a set of numbers all divide evenly into. They're inverses of each other, and related by the formula LCM(a, b) × GCF(a, b) = a × b.
Can the LCM of two numbers just be one of the numbers?
Yes — if one number is a multiple of the other, the LCM is simply the larger number. For example, LCM(4, 8) = 8, since 8 is already a multiple of 4.
Related Calculators
- GCF Calculator — General Math
- LCD Calculator — General Math
- Factors Calculator — General Math
- Square Root Calculator — General Math