Least common multiple

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The least common multiple of two integers is the smallest positive integer between all the multiples of both. It is usually written as LCM(a, b).[1] Likewise, the LCM of more than two integers is the smallest positive integer that is divisible by each of them.[2][3]

In elementary arithmetic, the LCM is also the "lowest common denominator" (LCD) that must be calculated, before fractions can be added, subtracted or compared.

Overview[change | change source]

A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2. By the same principle, 10 is the least common multiple of −5 and 2 as well.

Relation with the greatest common divisor[change | change source]

It is known that:

where is the greatest common divisor of a and b, This formula is often used to compute the LCD, by first finding the GCD of a and b.

Related pages[change | change source]

References[change | change source]

  1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-30.
  2. Weisstein, Eric W. "Least Common Multiple". mathworld.wolfram.com. Retrieved 2020-08-30.
  3. "Least Common Multiple". www.mathsisfun.com. Retrieved 2020-08-30.