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How It Works
The Least Common Multiple is the smallest positive integer divisible by both numbers. This calculator finds the GCF first using Euclid's algorithm, then computes LCM(a, b) = (a × b) / GCF(a, b). The LCM is essential for adding fractions with different denominators.
Example Problem
Find LCM(12, 18):
- GCF(12, 18) = 6
- LCM = (12 × 18) / 6 = 216 / 6 = 36
Frequently Asked Questions
How to find the LCM of two numbers?
The fastest method is to find the GCF first (using Euclid's algorithm), then divide the product of the two numbers by the GCF. For 8 and 12: GCF = 4, LCM = (8 × 12) / 4 = 24.
Why is LCM important for fractions?
The LCM of two denominators gives you the least common denominator (LCD) needed to add or subtract fractions. Using the LCD keeps numbers small and makes simplification easier.
Can the LCM equal one of the numbers?
Yes. If one number divides the other evenly, the LCM is the larger number. For example, LCM(4, 12) = 12 because 12 is already a multiple of 4.
Related Calculators
- GCF Calculator — find the Greatest Common Factor of two numbers.
- Fraction Addition Calculator — add fractions using the LCD.
- Fraction Subtraction Calculator — subtract fractions with step-by-step work.
- Fraction Multiplication Calculator — multiply fractions and simplify.
- GCF Calculator — GCF and LCM are related by LCM(a,b) = |a×b| / GCF(a,b).