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A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2.
For example, in the following problem: 79 • 26, by assigning subscripts of 1 to 79 and subscripts of 2 to 26, we would reach the answer as follows: Step 1 = (7 - 9) • 6 = -12 Step 2 = 9 • 2 = 18 Step 3 = (9 • 6) = 54 + 5 = 59. Steps 1-3 are added together to reach a sum of 65. Step 4 = 65@4 = 654 Step 5 = 70 • 20 = 1400 + 654 = 2054
A prime modulus requires the computation of a double-width product and an explicit reduction step. If a modulus just less than a power of 2 is used (the Mersenne primes 2 31 − 1 and 2 61 − 1 are popular, as are 2 32 − 5 and 2 64 − 59), reduction modulo m = 2 e − d can be implemented more cheaply than a general double-width division ...
The first step of the M-step algorithm is a = q 0 b + r 0, and the Euclidean algorithm requires M − 1 steps for the pair b > r 0. By induction hypothesis, one has b ≥ F M+1 and r 0 ≥ F M. Therefore, a = q 0 b + r 0 ≥ b + r 0 ≥ F M+1 + F M = F M+2, which is the desired inequality.
All the above multiplication algorithms can also be expanded to multiply polynomials. Alternatively the Kronecker substitution technique may be used to convert the problem of multiplying polynomials into a single binary multiplication. [31] Long multiplication methods can be generalised to allow the multiplication of algebraic formulae:
lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n). gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than computing gcd and lcm using other algorithms which do not require known prime factorization.
LCM may refer to: Computing and mathematics. Latent class model, a concept in statistics; Least common multiple, a function of two integers; Living Computer Museum;
The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of primary school or elementary school , this algorithm is sometimes called the grammar school method.
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