# Least Common Multiple

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## least common multiple

[′lēst ′käm·ən ′məl·tə·pəl]*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Least Common Multiple

The least common multiple (LCM) of two or several natural numbers is the smallest positive number exactly divisible by each of the given numbers. For example, the LCM of 2 and 3 is 6, and the LCM of 6, 8, 9, 15, and 20 is 360. Least common multiples are used in adding and subtracting fractions; the least common denominator of two or several fractions is the LCM of their denominators. If we know the prime factors of the given numbers, then the LCM of these numbers is the product of all the factors, each taken the greatest number of times it occurs in any one of the numbers. Thus 6 = 2.3, 8 = 2.2.2, 9 = 3.3, 15 = 3–5, and 20 = 2–2–5; therefore, the LCM of 6, 8, 9, 15, and 20 is 2.2.2.3.3.5 = 360. The concept of LCM is applicable not only to numbers; for example, the LCM of two or several polynomials is the polynomial of least degree divisible by each of the given polynomials.