GCD and LCM Integer Functions

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Description

Greatest common divisor and least common multiple

Usage

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gcd(a, b, extended = FALSE)
Lcm(a, b)

Arguments

a, b

vectors of integers.

extended

logical; if TRUE the extended Euclidean algorithm will be applied.

Details

Computation based on the extended Euclidean algorithm.

If both a and b are vectors of the same length, the greatest common divisor/lowest common multiple will be computed elementwise. If one is a vektor, the other a scalar, the scalar will be replicated to the same length.

Value

A numeric (integer) value or vector of integers. Or a list of three vectors named c, d, g, g containing the greatest common divisors, such that

g = c * a + d * b.

Note

The following relation is always true:

n * m = gcd(n, m) * lcm(n, m)

See Also

numbers::extGCD

Examples

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gcd(12, 1:24)
gcd(46368, 75025)  # Fibonacci numbers are relatively prime to each other
Lcm(12, 1:24)
Lcm(46368, 75025)  # = 46368 * 75025

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