In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the least common multiple of the denominators of a set of vulgar fractions. It is the smallest positive integer that is a multiple of each denominator in the set. The term has entered popular culture with a different non-mathematical meaning which indicates the least sophisticated element in a particular situation.
The LCD of
In Swami Bharati Krishna Tirtha's Vedic mathematics, the auxiliary fraction method is used to convert a fraction to its equivalent decimal representation. The "auxiliary fraction" is not a true fraction, but is simply a mnemonic aid used in the calculation. The method is essentially the long division algorithm adapted for mental calculation. It is simplest when the fraction's denominator is one less than a multiple of 10, when it uses the identity
Variants of the method used when the denominator is not one less than a multiple of 10 become progressively more complex but still in the realm of mental math or with one line of notation.
In arithmetic and number theory, the least common multiple (also called the lowest common multiple or smallest common multiple) of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a,0) for all a, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility.
The LCM is familiar from grade-school arithmetic as the "least common denominator" (LCD) that must be determined before fractions can be added, subtracted or compared.
Elementary arithmetic is the simplified portion of arithmetic which includes the operations of addition, subtraction, multiplication, and division.
Elementary arithmetic starts with the natural numbers and the written symbols (digits) which represent them. The process for combining a pair of these numbers with the four basic operations traditionally relies on memorized results for small values of numbers, including the contents of a multiplication table to assist with multiplication and division.