least common multiple

Let M be the least common multiple of all the m.

In a unique factorization domain, any two elements have a least common multiple.

First, take the least common multiple of the generators of the ideal.

However, any two least common multiples of the same pair of elements are associates.

All solutions x are then congruent modulo the least common multiple of the n.

They used least common multiples with unit fractions.

This continues, generating a total of 60 different terms (the least common multiple of ten and twelve), after which the cycle repeats itself.

We can calculate the block-length of the code by evaluating the least common multiple of and .

Others have suggested only one method was used by Ahmes which used multiplicative factors similar to least common multiples.

The second Chebyshev function is the logarithm of the least common multiple of the integers from 1 to n.

The exponent is given by the Carmichael function the least common multiple of the orders of the cyclic groups.

In this article we will denote the least common multiple of two integers a and b as lcm( a, b ).

The supremum of finite sets is given by the least common multiple and the infimum by the greatest common divisor.

Equivalently, any two non-zero elements of R have a least common multiple (LCM).

Any two (or finitely many) elements of a UFD have a greatest common divisor and a least common multiple.

The lowest common denominator of two vulgar fractions can be found by computing the least common multiple of their denominators.

Furthermore, under these conditions, the system has a unique solution in where , which denotes the least common multiple (LCM) of .

Book 7 deals strictly with elementary number theory: divisibility, prime numbers, Euclid's algorithm for finding the greatest common divisor, least common multiple.

The natural numbers form a distributive lattice (complete as a meet-semilattice) with the greatest common divisor as meet and the least common multiple as join.

The least upper bound of two numbers is the smallest number that is divided by both of them, i.e. the least common multiple of the numbers.

The following formula reduces the problem of computing the least common multiple to the problem of computing the greatest common divisor (GCD):

It consists of 532 common years, being the least common multiple of the numbers of years in the cycle of the sun and the cycle of the moon.

If k and k' have no common prime factors other than 2 and/or 5, then the period of equals the least common multiple of the periods of and .

IN the second chapter of his 1889 novel, "Sylvie and Bruno," Lewis Carroll suggested that the algebraic rule of the least common multiple should be ruthlessly applied to books.

This formula is often used to compute least common multiples: one first computes the gcd with Euclid's algorithm and then divides the product of the given numbers by their gcd.