Least Common Multiple

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Related to Least Common Multiple: least common denominator, greatest common factor

least common multiple

[′lēst ′käm·ən ′məl·tə·pəl]
The least common multiple of a set of quantities (for example, numbers or polynomials) is the smallest quantity divisible by each of them. Abbreviated lcm.

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 = 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.

References in periodicals archive ?
But doing your way of adding fractions, finding a least common multiple of the denominators .
In the the pseudocode on the Figure 4, the least common multiple of the selectable delivery cycles is calculated in the line 1.
In this environment, the maximum of the least common multiple of delivery cycles is 2520, and then the timetable for delivery is from time 0 to time 2519.
As an evaluated value, we calculated the load of each node, system total loads (SL), and fairness index (FI) among the time of the least common multiple of selectable delivery cycles.
I could generate polyrhythmic graphs of least common multiples or use computer models if I wanted (I didn't), but, in the end, human ears would judge the performance, so human ears should guide the learning process.
Since we will make connections between periodicity of trigonometric functions and the concepts of greatest common divisor and the least common multiple that are defined only for integers, we need to provide extended definition of the terms "divisor", "multiple", "greatest common divisor" and the "least common multiple" of rational numbers.
A rational positive number m is said to be the least common multiple of a and b if m is a multiple of both a and b and if c is any other common multiple of a and b, then m [less than or equal to] c.
Following the definitions 4-6 above, we denote by (a, b) the greatest common divisor (GCD) of the rational numbers a and b, and by [ a, b] the least common multiple (LCM) of the nonzero rational numbers a and b.
They will also develop a conceptual understanding of equivalent fractions and least common multiples instead of merely memorizing rules or algorithms.