Greatest Common Divisor and Least Common Multiple

Calculates the greatest common divisor (GCD) and least common multiple (LCM) of all the values present in its arguments.

GCD(..., na.rm = FALSE)
LCM(..., na.rm = FALSE)

Arguments

...

integer or logical vectors.

na.rm

logical. Should missing values (including NaN) be removed?

Details

The computation is based on the Euclidean algorithm without using the extended version.The greatest common divisor for all numbers in the integer vector x will be computed (the multiple GCD).

Value

A numeric (integer) value.

Note

The following relation is always true:

n * m = GCD(n, m) * LCM(n, m)

References

Eddelbuettel, D. (2013). Seamless R and C++ Integration with Rcpp. New York, NY: Springer.

Author

Dirk Eddelbuettel <edd@debian.org> (RCPP part), Andri Signorell <andri@signorell.net>, originally based on code in package numbers by Hans W Borchers <hwborchers@googlemail.com>

See also

Factorize, Primes, IsPrime

Examples

GCD(12, 10)
#> [1] 2
GCD(144, 233)    # Fibonacci numbers are relatively prime to each other
#> [1] 1

LCM(12, 10)
#> [1] 60
LCM(144, 233)    # = 144 * 233
#> [1] 33552

# all elements will be flattened by unlist
GCD(2, 3, c(5, 7) * 11)
#> [1] 1
GCD(c(2*3, 3*5, 5*7))
#> [1] 1
LCM(c(2, 3, 5, 7) * 11)
#> [1] 2310
LCM(2*3, 3*5, 5*7)
#> [1] 210