GCD and LCM Euclidean Algorithm in DSA C# - 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 C#

int GCD(int a, int b) {
    while (b != 0) {
        int temp = b;
        b = a [1] b;
        a = temp;
    }
    return a;
}

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

A%

B-

C/

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction instead of remainder operator.

Using division '/' which returns quotient, not remainder.

The Euclidean algorithm uses the remainder operator '%' to find the GCD by repeatedly replacing the larger number with the remainder of the division.

2fill in blank

medium

Complete the code to calculate the Least Common Multiple (LCM) of two numbers using their GCD.

DSA C#

int LCM(int a, int b) {
    return (a [1] b) / GCD(a, b);
}

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

A+

B/

C-

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Adding numbers instead of multiplying.

Dividing numbers before multiplying.

LCM is calculated by multiplying the two numbers and dividing by their GCD.

3fill in blank

hard

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

DSA C#

int GCD(int a, int b) {
    while (b != 0) {
        int temp = a;
        a = b;
        b = [1];
    }
    return a;
}

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

Atemp % a

Ba % b

Ctemp % b

Dtemp % temp

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'a % b' after 'a' has been updated.

Using 'temp % temp' which is always zero.

The remainder should be calculated as temp % b, where temp holds the old value of a.

4fill in blank

hard

Fill both blanks to create a dictionary that maps numbers to their GCD with 12, only if the GCD is greater than 1.

DSA C#

var gcdMap = new Dictionary<int, int>();
int[] numbers = {2, 3, 4, 5, 6};
foreach (var num in numbers) {
    int gcd = GCD(num, 12);
    if (gcd [1] 1) {
        gcdMap.Add(num, [2]);
    }
}

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

A>

B==

C<

Dgcd

Attempts:

3 left

💡 Hint

Common Mistakes

Using '==' instead of '>' in the condition.

Adding 'num' instead of 'gcd' as the dictionary value.

We check if gcd is greater than 1, then add the number and its gcd to the dictionary.

5fill in blank

hard

Fill all three blanks to create a method that returns a dictionary mapping numbers to their LCM with 10, only if the LCM is less than 50.

DSA C#

Dictionary<int, int> GetLCMMap(int[] nums) {
    var lcmMap = new Dictionary<int, int>();
    foreach (var n in nums) {
        int lcm = LCM(n, 10);
        if (lcm [1] 50) {
            lcmMap.Add([2], [3]);
        }
    }
    return lcmMap;
}

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

A<

Bn

Clcm

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<' in the condition.

Swapping key and value in the dictionary add.

We check if lcm is less than 50, then add the number and its lcm to the dictionary.

Practice

1. What does the Euclidean algorithm primarily calculate between two numbers a and b?

easy

A. The difference between a and b

B. The Greatest Common Divisor (GCD)

C. The sum of a and b

D. The Least Common Multiple (LCM)

Solution

1. Step 1: Understand the Euclidean algorithm purpose

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

2. Step 2: Differentiate GCD from LCM

   While GCD finds the largest number dividing both, LCM finds the smallest number divisible by both. The Euclidean algorithm directly calculates GCD.

3. Final Answer:

   The Greatest Common Divisor (GCD) -> Option B

4. Quick Check:

   Euclidean algorithm = GCD [OK]

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

Common Mistakes:

• Confusing GCD with LCM
• Thinking it calculates sum or difference
• Assuming it finds prime factors directly

2. Which of the following is the correct C# syntax to calculate the GCD of two integers a and b using the built-in method?

easy

A. int gcd = Math.GreatestCommonDivisor(a, b);

B. int gcd = Math.GCD(a, b);

C. int gcd = Math.gcd(a, b);

D. int gcd = Math.Gcd(a, b);

Solution

1. Step 1: Identify the correct method name in C#

   The .NET 6+ Math class provides the method Math.Gcd(int, int) to calculate the greatest common divisor.

2. Step 2: Check method name casing and spelling

   Method names in C# are PascalCase, so Math.Gcd is correct, while others are incorrect or do not exist.

3. Final Answer:

   int gcd = Math.Gcd(a, b); -> Option D

4. Quick Check:

   Correct method is Math.Gcd [OK]

Hint: Use Math.Gcd with capital G and C# PascalCase [OK]

Common Mistakes:

• Using incorrect method names like Math.gcd or Math.GCD
• Assuming method is GreatestCommonDivisor
• Wrong casing causing compile errors

3. What is the output of the following C# code?

int a = 48;
int b = 18;
int gcd = Math.Gcd(a, b);
int lcm = (a * b) / gcd;
Console.WriteLine($"GCD: {gcd}, LCM: {lcm}");

medium

A. GCD: 18, LCM: 48

B. GCD: 12, LCM: 72

C. GCD: 6, LCM: 144

D. GCD: 3, LCM: 288

Solution

1. Step 1: Calculate GCD of 48 and 18

   Using Euclidean algorithm: 48 % 18 = 12, 18 % 12 = 6, 12 % 6 = 0, so GCD = 6.

2. Step 2: Calculate LCM using formula

   LCM = (48 * 18) / 6 = 864 / 6 = 144.

3. Final Answer:

   GCD: 6, LCM: 144 -> Option C

4. Quick Check:

   GCD=6, LCM=144 [OK]

Hint: LCM = (a * b) / GCD always [OK]

Common Mistakes:

• Calculating GCD incorrectly
• Swapping GCD and LCM values
• Forgetting to divide product by GCD for LCM

4. Identify the error in this C# code snippet that tries to compute the GCD using Euclidean algorithm:

int Gcd(int a, int b) {
    while (b != 0) {
        int temp = a % b;
        a = b;
        b = temp;
    }
    return b;
}

medium

A. Returns b instead of a after loop ends

B. Uses wrong operator for remainder

C. Infinite loop because b never changes

D. Missing base case for zero inputs

Solution

1. Step 1: Trace the Euclidean algorithm loop

   The loop updates a and b until b becomes zero. At loop end, a holds the GCD.

2. Step 2: Check return statement correctness

   The code returns b, which is zero at loop end. It should return a which holds the GCD.

3. Final Answer:

   Returns b instead of a after loop ends -> Option A

4. Quick Check:

   Return a after loop [OK]

Hint: Return 'a' after loop, not 'b' [OK]

Common Mistakes:

• Returning the wrong variable after loop
• Confusing remainder operator with division
• Not updating variables inside loop

5. Given two arrays A = [12, 15, 21] and B = [18, 35, 14], which C# code snippet correctly computes an array of LCMs for each pair (A[i], B[i]) using the Euclidean algorithm?

hard

A. int[] lcms = new int[A.Length];
for (int i = 0; i < A.Length; i++) {
int gcd = Math.Gcd(A[i], B[i]);
lcms[i] = (A[i] * B[i]) / gcd;
}

B. int[] lcms = new int[A.Length];
for (int i = 0; i < A.Length; i++) {
int gcd = Math.Gcd(A[i], B[i]);
lcms[i] = gcd * A[i] * B[i];
}

C. int[] lcms = new int[A.Length];
for (int i = 0; i < A.Length; i++) {
lcms[i] = Math.Gcd(A[i], B[i]);
}

D. int[] lcms = new int[A.Length];
for (int i = 0; i < A.Length; i++) {
lcms[i] = (A[i] + B[i]) / Math.Gcd(A[i], B[i]);
}

Solution

1. Step 1: Calculate GCD for each pair

   Use Math.Gcd(A[i], B[i]) to find the greatest common divisor for each pair.

2. Step 2: Compute LCM using formula

   LCM = (A[i] * B[i]) / GCD. Store this in the lcms array at index i.

3. Final Answer:

   Option A code snippet correctly computes LCM array -> Option A

4. Quick Check:

   LCM = (a*b)/GCD for each pair [OK]

Hint: LCM = (a*b)/GCD for each pair in loop [OK]

Common Mistakes:

• Multiplying GCD with product instead of dividing
• Assigning GCD instead of LCM to result array
• Using sum instead of product in LCM formula