Least common multiple

Related BrainMass Solutions

• Ring Theory: Euclidean Rings and Elements with Least Common Multiples

  105914 Euclidean Rings and Elements with Least Common Multiples Given two elements a, b in the Euclidean ring R their least common multiple cЄR is an element in R such that a│c and b│c and such that whenever a│x and

• Euclidean Rings and GCD

  106672 Ring Theory : Euclidean Rings and GCD If the least common multiple of a and b in the Euclidean ring R is denoted by [a,b], prove that [a,b] = ab/(a, b) where (a, b) is the greatest common divisor of a

• Least common multiples

  We call an integer m the least common multiple of n provided (1) m is positive, (2) m is a common multiple of a and b, and (3) if n is any other positive common multiple of a and b, then n [greater than or equal to] m.

• Unique Factorization Prime/Co-Prime

  Recall [a,m] is the least common multiple. Suppose a can divide m, then m is a multiple of a. Notice m is also a multiple of itself. Hence m is a common multiple of a,m. But for any multiple of m, it must be at least m.

• If R is a unique factorization domain and if a,b are in R, then a and b have a least common multiple (l.c.m.) in R.

  This solution is comprised of a detailed explanation of least common multiple (l.c.m.) of a and b in R.

• Well-Ordering and Division Theorem

  Now m is the least common multiple of a, b, r is another common multiple of a, b with 0 < r < m.

• Mathematics - Algebra

  202577 Mathematics - Finding the Least Common Multiple Find the least commong multiple of two expressions ..... (see attachment for equations) The solution file is attached.

• Disjoint cycles and least common multiple

  There are two proofs here regarding least common multiple of disjoint cycles.

• Computing greatest common divisor and least common multiple

  It is not possible to do so because their GCD is 3, so their Least Common Multiple (LCM) is 9*15/3=45 which is not 225. The solution gives detailed steps on computing a greatest common divisor and a least common multiple.