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LCM Calculator

The Least Common Multiple (LCM) is the smallest positive integer that is a multiple of two or more given integers. Our calculator helps you find it quickly, which is super handy for adding or subtracting fractions with different denominators.

Enter two or more positive integers, separated by commas or spaces (e.g., 12, 18, 24)

How it works

The Least Common Multiple (LCM) is the smallest positive integer that is a multiple of two or more given integers. Our calculator helps you find it quickly, which is super handy for adding or subtracting fractions with different denominators.


The Formula
To find the LCM of two numbers, say 'a' and 'b', you can use the formula: LCM(a, b) = |a * b| / GCD(a, b). For more than two numbers, you can find the LCM iteratively: LCM(a, b, c) = LCM(LCM(a, b), c).

Worked Example
  1. LCM of 4, 6, and 10

    Let's find the LCM of 4, 6, and 10. First, list multiples of each number: Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60. Multiples of 10: 10, 20, 30, 40, 50, 60. The smallest number that appears in all three lists is 60. So, LCM(4, 6, 10) = 60.


Tips, Assumptions & Limitations
  • Enter numbers separated by commas or spaces.
  • The LCM is crucial for adding and subtracting fractions.
  • It's always a positive integer.
  • Use prime factorization for larger numbers.
FAQ

The LCM is the smallest positive number that is a multiple of two or more given numbers. Think of it as the first number they all 'meet' at when you list out their multiples.

The LCM is super useful when you need to add or subtract fractions with different denominators. You find the LCM of the denominators to get a common denominator, making the fractions easy to combine.

You can list out the multiples of each number until you find the smallest one they share. For example, for 3 and 5, multiples of 3 are 3, 6, 9, 12, 15. and multiples of 5 are 5, 10, 15. The LCM is 15.

Yes, absolutely! Just enter all the numbers you want to find the LCM for, separated by commas or spaces, and the calculator will do the rest.

Companion article

LCM Calculator Explained: Find the Least Common Multiple

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