Mathematical Programs

Learn mathematical programs through an executable example, then connect the small demonstration to production code.

Mathematical programming exercises combine arithmetic, loops and reusable functions. The greatest common divisor (GCD) is a useful example of an efficient iterative algorithm.

Euclid’s algorithm repeatedly replaces a pair of numbers with the second number and their remainder until the second number becomes zero.

Follow this diagram before executing the example. Check where a value or decision changes what runs next.

This example is a complete program. Save it as main.go or paste it into the Go Playground.

Go code

package main

import "fmt"

func gcd(a, b int) int {
	if a < 0 {
		a = -a
	}
	if b < 0 {
		b = -b
	}
	for b != 0 {
		a, b = b, a%b
	}
	return a
}
func main() { fmt.Println("GCD:", gcd(84, 30)); fmt.Println("LCM:", 84/gcd(84, 30)*30) }

Output

GCD: 6
LCM: 420

gcd(84,30) computes 6 using remainder steps. Dividing first and then multiplying yields 420 as the least common multiple for these positive inputs.

• The LCM formula must account for zero inputs and potential integer overflow.
• Use floating-point arithmetic only when it matches the problem’s required precision.

Calculate the GCD and LCM of 24 and 36, then handle an input pair containing zero.

Tip: Edit the example above, predict the output, and run the modified code to test your reasoning.

You have practiced Mathematical Programs in a small, self-contained program. The important habit is to predict what runs, inspect the actual output and distinguish the language rule from the particular example.

Before continuing, make sure you can explain the program to someone who has not seen it, including the line that changes its result.