Time and Numeric Utilities

GCD LCM

Greatest common divisor and least common multiple help compare repeating numeric sizes.

gcd `std::gcd` finds the largest integer that divides two values evenly.
lcm `std::lcm` finds the smallest positive integer that is a multiple of both values.

GCD LCM

width
gcd_lcm.cpp
Replay: real traced execution (multi-file project)
#include <iostream>
#include <numeric>

int main() {
    int width = 12;

    int height = 8;
    int common = std::gcd(width, height);
    int repeat = std::lcm(width, height);

    std::cout << "width=" << width << std::endl;
    std::cout << "gcd=" << common << std::endl;
    std::cout << "lcm=" << repeat << std::endl;
    return 0;
}

#include <iostream>
#include <numeric>

int main() {
    int width = 7;

    int height = 8;
    int common = std::gcd(width, height);
    int repeat = std::lcm(width, height);

    std::cout << "width=" << width << std::endl;
    std::cout << "gcd=" << common << std::endl;
    std::cout << "lcm=" << repeat << std::endl;
    return 0;
}

#include <iostream>
#include <numeric>

int main() {
    int width = 18;

    int height = 8;
    int common = std::gcd(width, height);
    int repeat = std::lcm(width, height);

    std::cout << "width=" << width << std::endl;
    std::cout << "gcd=" << common << std::endl;
    std::cout << "lcm=" << repeat << std::endl;
    return 0;
}

  1. width ← 12, height ← 8, common ← 4, repeat ← 24

    4int main() {5    int width→ 12 = 12; //@width=18, 767    int height→ 8 = 8;8    int common→ 4 = std::gcd(width12, height8);9    int repeat→ 24 = std::lcm(width12, height8);1011    std::cout << "width=" << width12 << std::endl;12    std::cout << "gcd=" << common4 << std::endl;13    std::cout << "lcm=" << repeat24 << std::endl;14    return 0;15}
    outputwidth=12
gcd=4
lcm=24

  1. width ← 7, height ← 8, common ← 1, repeat ← 56

    4int main() {5    int width→ 7 = 7;67    int height→ 8 = 8;8    int common→ 1 = std::gcd(width7, height8);9    int repeat→ 56 = std::lcm(width7, height8);1011    std::cout << "width=" << width7 << std::endl;12    std::cout << "gcd=" << common1 << std::endl;13    std::cout << "lcm=" << repeat56 << std::endl;14    return 0;15}
    outputwidth=7
gcd=1
lcm=56

  1. width ← 18, height ← 8, common ← 2, repeat ← 72

    4int main() {5    int width→ 18 = 18;67    int height→ 8 = 8;8    int common→ 2 = std::gcd(width18, height8);9    int repeat→ 72 = std::lcm(width18, height8);1011    std::cout << "width=" << width18 << std::endl;12    std::cout << "gcd=" << common2 << std::endl;13    std::cout << "lcm=" << repeat72 << std::endl;14    return 0;15}
    outputwidth=18
gcd=2
lcm=72