Number theory
LCM Calculator
Find the least common multiple of any integers.
Least Common Multiple
24
GCD2
Product192
LCM × GCD = product of numbers. Useful for scheduling, fractions, and periodic cycles.
Number theory
Find the least common multiple of any integers.
Least Common Multiple
24
LCM × GCD = product of numbers. Useful for scheduling, fractions, and periodic cycles.
The Least Common Multiple (LCM) is the smallest positive integer that is evenly divisible by two or more numbers without leaving a remainder. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into equally.
The calculator finds the LCM by identifying all prime factors of each number, then multiplying together the highest power of each prime that appears. Alternatively, it can use the mathematical relationship: LCM(a, b) = (a × b) ÷ GCD(a, b), where GCD is the Greatest Common Divisor. For more than two numbers, the process repeats pairwise until all numbers are combined.
LCM(a, b) = (a × b) ÷ GCD(a, b)Multiply the two numbers and divide by their Greatest Common Divisor. The GCD is the largest number that divides both evenly. This relationship holds true for any pair of positive integers.
| Input | Result | Notes |
|---|---|---|
| 12 and 18 | 36 | 12 = 2² × 3; 18 = 2 × 3². Taking highest powers: 2² × 3² = 36. |
| 4, 6, and 8 | 24 | First find LCM(4, 6) = 12, then LCM(12, 8) = 24. All three divide evenly into 24. |
| 5 and 7 | 35 | Since 5 and 7 are both prime and share no common factors, LCM = 5 × 7. |
LCM (Least Common Multiple) is the smallest number both divide into; GCD (Greatest Common Divisor) is the largest number that divides both. For 12 and 18: LCM = 36, GCD = 6.
Yes. Calculate the LCM of the first two, then find the LCM of that result and the third number, and repeat for any additional numbers.
The LCM of denominators becomes your least common denominator, which keeps numerators small and final answers in simplest form.
LCM is only defined for positive integers. Zero has no LCM, and negative numbers are treated by their absolute value (positive form).
Yes, they are identical terms. 'Least' and 'lowest' both mean the smallest positive multiple that works.
Scheduling (when two repeating events coincide), carpooling, production cycles, and any synchronization problem where you need events to align.