GCD and LCM Euclidean Algorithm in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the greatest common divisor (GCD) of two numbers using the Euclidean algorithm.

DSA Rust

fn gcd(mut a: i32, mut b: i32) -> i32 {
    while b != 0 {
        let temp = b;
        b = a [1] b;
        a = temp;
    }
    a
}

Drag options to blanks, or click blank then click option'

A/

B%

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using division (/) instead of modulus (%) causes incorrect results.

Using subtraction (-) instead of modulus (%) is less efficient.

The Euclidean algorithm uses the remainder operation (%) to update b with the remainder of a divided by b.

2fill in blank

medium

Complete the code to calculate the least common multiple (LCM) of two numbers using the GCD function.

DSA Rust

fn lcm(a: i32, b: i32) -> i32 {
    (a * b) [1] gcd(a, b)
}

Drag options to blanks, or click blank then click option'

A+

B-

C%

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition (+) instead of division (/) leads to wrong results.

Using modulus (%) or subtraction (-) is incorrect here.

LCM is calculated by dividing the product of the two numbers by their GCD.

3fill in blank

hard

Fix the error in the gcd function to correctly swap values during the Euclidean algorithm.

DSA Rust

fn gcd(mut a: i32, mut b: i32) -> i32 {
    while b != 0 {
        let temp = a;
        a = b;
        b = [1];
    }
    a
}

Drag options to blanks, or click blank then click option'

Atemp % a

Ba % b

Ctemp % b

Db % temp

Attempts:

3 left

💡 Hint

Common Mistakes

Using a % b after a is updated causes wrong remainder.

Using temp % a is incorrect because a has changed.

After swapping, b should be updated to the remainder of the old a (temp) divided by b.

4fill in blank

hard

Fill both blanks to create a function that returns a tuple with GCD and LCM of two numbers.

DSA Rust

fn gcd_lcm(a: i32, b: i32) -> (i32, i32) {
    let gcd_value = gcd(a, b);
    let lcm_value = (a * b) [1] gcd_value;
    ([2], lcm_value)
}

Drag options to blanks, or click blank then click option'

A/

Bgcd_value

Ca

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 'a' instead of gcd_value in the tuple.

Using multiplication (*) instead of division (/) for LCM.

LCM is product divided by GCD, and the tuple returns (GCD, LCM).

5fill in blank

hard

Fill all three blanks to implement a recursive GCD function and use it to compute LCM.

DSA Rust

fn gcd_recursive(a: i32, b: i32) -> i32 {
    if b == 0 {
        [1]
    } else {
        gcd_recursive(b, a [2] b)
    }
}

fn lcm_using_recursive(a: i32, b: i32) -> i32 {
    (a * b) [3] gcd_recursive(a, b)
}

Drag options to blanks, or click blank then click option'

Aa

B%

C/

Db

Attempts:

3 left

💡 Hint

Common Mistakes

Returning b instead of a in base case.

Using subtraction (-) instead of modulus (%) in recursion.

Using multiplication (*) instead of division (/) for LCM.

Base case returns a; recursive call uses modulus (%); LCM divides product by GCD.

Practice

1. What does the Euclidean algorithm primarily calculate when given two positive integers a and b?

easy

A. The greatest common divisor (GCD) of a and b

B. The least common multiple (LCM) of a and b

C. The sum of a and b

D. The difference between a and b

Solution

1. Step 1: Understand Euclidean algorithm purpose

   The Euclidean algorithm is designed to find the greatest common divisor (GCD) of two integers by repeatedly applying the remainder operation.

2. Step 2: Differentiate GCD from LCM

   While GCD is the largest number dividing both without remainder, LCM is the smallest number divisible by both. Euclidean algorithm directly finds GCD.

3. Final Answer:

   The greatest common divisor (GCD) of a and b -> Option A

4. Quick Check:

   Euclidean algorithm = GCD [OK]

Hint: Euclidean algorithm finds GCD, not LCM or sums [OK]

Common Mistakes:

• Confusing GCD with LCM
• Thinking it calculates sum or difference
• Assuming it returns both GCD and LCM

2. Which of the following Rust function signatures correctly represents a function to compute the GCD of two unsigned integers using the Euclidean algorithm?

easy

A. fn gcd(a: u32, b: u32) -> u32

B. fn gcd(a: i32, b: i32) -> i32

C. fn gcd(a: u32, b: u32) -> bool

D. fn gcd(a: u32, b: u32)

Solution

1. Step 1: Identify correct parameter and return types

   GCD function takes two unsigned integers (u32) and returns an unsigned integer (u32) representing the GCD.

2. Step 2: Check function signature correctness

   fn gcd(a: u32, b: u32) -> u32 matches this: inputs are u32, output is u32. fn gcd(a: i32, b: i32) -> i32 uses signed integers, which is less common for GCD. fn gcd(a: u32, b: u32) -> bool returns bool, incorrect. fn gcd(a: u32, b: u32) lacks return type.

3. Final Answer:

   fn gcd(a: u32, b: u32) -> u32 -> Option A

4. Quick Check:

   Correct signature returns u32 [OK]

Hint: GCD inputs and output are unsigned integers [OK]

Common Mistakes:

• Using signed integers instead of unsigned
• Missing return type in function signature
• Returning wrong type like bool

3. What is the output of the following Rust code snippet?

fn gcd(mut a: u32, mut b: u32) -> u32 {
    while b != 0 {
        let temp = b;
        b = a % b;
        a = temp;
    }
    a
}

fn main() {
    let result = gcd(48, 18);
    println!("{}", result);
}

medium

A. 12

B. 6

C. 18

D. 3

Solution

1. Step 1: Trace Euclidean algorithm steps for gcd(48, 18)

   Start with a=48, b=18. Compute remainder: 48 % 18 = 12. Update a=18, b=12. Next, 18 % 12 = 6. Update a=12, b=6. Then, 12 % 6 = 0. Update a=6, b=0.

2. Step 2: Identify when loop ends and return value

   Loop ends when b=0. Return a=6 as GCD.

3. Final Answer:

   6 -> Option B

4. Quick Check:

   GCD(48,18) = 6 [OK]

Hint: Use remainder steps until second number is zero [OK]

Common Mistakes:

• Returning the last remainder instead of last non-zero divisor
• Mixing up a and b updates
• Stopping loop too early

4. The following Rust function is intended to compute the LCM of two numbers using their GCD. Identify the error.

fn gcd(mut a: u32, mut b: u32) -> u32 {
    while b != 0 {
        let temp = b;
        b = a % b;
        a = temp;
    }
    a
}

fn lcm(a: u32, b: u32) -> u32 {
    a * b / gcd(a, b)
}

fn main() {
    println!("{}", lcm(0, 0));
}

medium

A. Wrong function signature for LCM

B. Incorrect GCD calculation logic

C. Missing return statement in LCM function

D. Division by zero error when both inputs are zero

Solution

1. Step 1: Analyze the LCM call with zero inputs

   The LCM function computes (a * b) / gcd(a, b). The main calls lcm(0, 0), where gcd(0, 0) returns 0, leading to division by zero.

2. Step 2: Verify gcd(0, 0) behavior

   In gcd, when a=0, b=0, the while loop doesn't execute (b == 0), so it returns a = 0.

3. Final Answer:

   Division by zero error when both inputs are zero -> Option D

4. Quick Check:

   LCM divides by gcd; gcd(0,0)=0 causes error [OK]

Hint: Check zero inputs cause gcd=0 leading to division error [OK]

Common Mistakes:

• Ignoring zero inputs causing division by zero
• Assuming gcd never returns zero
• Not validating inputs before LCM calculation

5. Given a list of positive integers [12, 15, 20], which Rust code snippet correctly computes their LCM using the Euclidean algorithm for GCD?

hard

A. let lcm = nums.iter().fold(1, |acc, &x| gcd(acc, x));

B. let lcm = nums.iter().fold(0, |acc, &x| acc + x / gcd(acc, x));

C. let lcm = nums.iter().fold(1u32, |acc, &x| acc * x / gcd(acc, x));

D. let lcm = nums.iter().fold(1, |acc, &x| acc * x * gcd(acc, x));

Solution

1. Step 1: Understand LCM folding logic

   LCM of multiple numbers can be found by folding with formula: lcm(a,b) = a * b / gcd(a,b). Starting with 1u32, fold applies this stepwise.

2. Step 2: Analyze each option

   let lcm = nums.iter().fold(1u32, |acc, &x| acc * x / gcd(acc, x)); correctly folds with acc * x / gcd(acc, x). let lcm = nums.iter().fold(0, |acc, &x| acc + x / gcd(acc, x)); uses addition, incorrect. let lcm = nums.iter().fold(1, |acc, &x| gcd(acc, x)); returns gcd only, not LCM. let lcm = nums.iter().fold(1, |acc, &x| acc * x * gcd(acc, x)); multiplies by gcd, incorrect.

3. Final Answer:

   let lcm = nums.iter().fold(1u32, |acc, &x| acc * x / gcd(acc, x)); -> Option C

4. Quick Check:

   Fold with acc * x / gcd(acc, x) computes LCM [OK]

Hint: Fold with acc * x / gcd(acc, x) to get LCM of list [OK]

Common Mistakes:

• Using addition instead of multiplication
• Returning gcd instead of LCM
• Multiplying by gcd instead of dividing