Find the Least Common Multiple of two or more numbers.
Enter two or more positive integers separated by commas.
Least Common Multiple
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Enter numbers to see LCM and prime factorization.
The LCM Calculator finds the Least Common Multiple of two or more positive integers. Enter your numbers separated by commas, and the calculator returns the smallest number that is divisible by all of them. The calculator also displays the prime factorization of each input so you can verify the result by hand using the standard method.
For small numbers, list multiples of each until you find a common one. Multiples of 4: 4, 8, 12, 16, 20, 24... Multiples of 6: 6, 12, 18, 24... LCM(4, 6) = 12.
LCM = product of highest power of each prime factor
For 12 and 18: 12 = 2² × 3, 18 = 2 × 3². Take the highest power of each prime: 2² × 3² = 4 × 9 = 36. So LCM(12, 18) = 36.
LCM(a, b) = (a × b) ÷ GCD(a, b)
This is the fastest method for two numbers if you know the GCD. LCM(12, 18) = (12 × 18) ÷ GCD(12, 18) = 216 ÷ 6 = 36.
Find LCM(15, 20, 30):
Verify: 60 ÷ 15 = 4 ✓, 60 ÷ 20 = 3 ✓, 60 ÷ 30 = 2 ✓.
The most common use of LCM is finding a common denominator when adding or subtracting fractions. To add 1/4 + 1/6, you need the LCM of 4 and 6, which is 12. Convert: 3/12 + 2/12 = 5/12. Without LCM, you would use 24 (4 × 6) as the denominator, get 6/24 + 4/24 = 10/24, and then need to simplify — more work for the same answer.
LCM also appears in scheduling problems. If bus A arrives every 8 minutes and bus B every 12 minutes, they arrive together every LCM(8, 12) = 24 minutes. If three machines cycle every 6, 9, and 15 seconds respectively, they all align every LCM(6, 9, 15) = 90 seconds. Any "when will these repeating events coincide?" question is an LCM problem in disguise.
LCM (Least Common Multiple) is the smallest positive integer that is divisible by each of the given numbers. For example, LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6.
Two common methods: (1) list multiples of each number until you find a common one; (2) use prime factorization and take the highest power of each prime. The calculator uses method 2.
For any two numbers a and b: LCM(a, b) × GCD(a, b) = a × b. This means LCM(a, b) = (a × b) ÷ GCD(a, b).
LCM is used to add/subtract fractions (finding common denominators), schedule repeating events, and solve word problems involving cycles. Example: if bell A rings every 4 min and bell B every 6 min, they ring together every LCM(4,6)=12 minutes.
Yes. LCM(a, b, c) = LCM(LCM(a, b), c). The calculator handles any number of inputs separated by commas.
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