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In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.
The least common multiple of the denominators of two fractions is the "lowest common denominator" (lcd), and can be used for adding, subtracting or comparing the fractions. The least common multiple of more than two integers a , b , c , . . . , usually denoted by lcm( a , b , c , . . .) , is defined as the smallest positive integer that is ...
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
In mathematics a rational number is a number that can be ... This definition derives from the fact that the ancient ... This is called the least common denominator.
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For set representing all notes of a major triad: [1 5 ⁄ 4 3 ⁄ 2] the LCD is 4 therefore T = 4 ⁄ f. For set representing all notes of a minor triad: [1 6 ⁄ 5 3 ⁄ 2] the LCD is 10 therefore T = 10 ⁄ f. If no least common denominator exists, for instance if one of the above elements were irrational, then the wave would not be periodic. [4]
An electronic pocket calculator with a seven-segment liquid-crystal display (LCD) that can perform arithmetic operations A modern scientific calculator with an LCD. An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.
In mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as representative; however, the usual representative is the least positive residue, the smallest non-negative integer that belongs to that class (i.e., the remainder of the Euclidean division). [2]