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Least Common Multiple
Calculate the Least Common Multiple (LCM) of two or more numbers using multiple methods. Get step-by-step solutions with listing multiples, prime factorization, and GCF formula.
Enter 2 or more positive integers
Enter numbers to find their LCM
Example: LCM(12, 18)
This relationship shows how LCM and GCF are inversely related.
Type two or more positive integers separated by commas. For example: 4, 6, 8
Click the "Calculate LCM" button to see the least common multiple and detailed step-by-step solutions using three different methods.
Compare the three methods to understand how LCM is calculated. Each method provides complete working steps for educational purposes.
List multiples of each number until you find the first common multiple.
Find prime factors and take the highest power of each prime.
Use LCM = (a × b) / GCF(a, b) for efficient calculation.
The Least Common Multiple (LCM) is the smallest positive integer that is divisible by two or more numbers. It's essential for adding or subtracting fractions with different denominators, finding patterns in repeating events, and scheduling problems. For example, if one event happens every 4 days and another every 6 days, they'll coincide every 12 days (the LCM).
For any two numbers a and b, there's a fundamental relationship: LCM(a,b) × GCF(a,b) = a × b. This means if you know the GCF, you can easily calculate the LCM using the formula LCM = (a × b) / GCF. They're inversely related - a larger GCF means a smaller LCM, and vice versa.
No, the LCM is always greater than or equal to the largest number in your set. At minimum, the LCM equals the largest number (when it's a multiple of all others). For example, LCM(3, 6, 12) = 12 because 12 is divisible by both 3 and 6.
The LCM of two prime numbers is always their product, since prime numbers have no common factors except 1. For example, LCM(3, 7) = 21, LCM(5, 11) = 55. This is because their GCF is 1, so LCM = (a × b) / 1 = a × b.
To find the LCM of fractions, find the LCM of the numerators and divide by the GCF of the denominators. Formula: LCM(a/b, c/d) = LCM(a,c) / GCF(b,d). However, for adding fractions, you typically need the LCD (Least Common Denominator), which is just the LCM of the denominators.
LCD (Least Common Denominator) is specifically the LCM of the denominators of fractions. LCD is just a special application of LCM used when adding or subtracting fractions. For example, to add 1/4 + 1/6, you need LCD(4,6) = LCM(4,6) = 12, so you convert to 3/12 + 2/12 = 5/12.
The Least Common Multiple (LCM) is a fundamental concept in mathematics that represents the smallest number that is a multiple of two or more integers. It's crucial for fraction operations, pattern recognition, and solving real-world synchronization problems.