GCD and LCM Euclidean Algorithm in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return the smaller of two numbers.

DSA Typescript

function min(a: number, b: number): number {
  return a [1] b ? a : b;
}

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

A<

B>

C==

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<' will return the larger number.

Using '==' will not compare sizes.

The function returns 'a' if a is less than b, otherwise b. So the operator should be '<'.

2fill in blank

medium

Complete the code to calculate the remainder of division.

DSA Typescript

function remainder(a: number, b: number): number {
  return a [1] b;
}

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

A/

B*

C%

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using '/' returns the quotient, not remainder.

Using '*' or '-' are arithmetic but not for remainder.

The '%' operator returns the remainder of dividing 'a' by 'b'.

3fill in blank

hard

Fix the error in the recursive GCD function to correctly call itself.

DSA Typescript

function gcd(a: number, b: number): number {
  if (b === 0) {
    return a;
  }
  return gcd([1], b);
}

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

Ab % a

Ba % b

Ca - b

Db - a

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping arguments incorrectly.

Using subtraction instead of modulo.

The Euclidean algorithm calls gcd with (b, a % b). Here, the first argument should be 'a % b' to reduce the problem.

4fill in blank

hard

Complete the code to compute the LCM using GCD.

DSA Typescript

function lcm(a: number, b: number): number {
  return (a [1] b) / gcd(a, b , 0);
}

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

A*

B+

C,

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' instead of '*'.

Missing comma between gcd arguments.

LCM is calculated as (a * b) divided by gcd(a, b). The gcd function needs both arguments separated by a comma.

5fill in blank

hard

Fill both blanks to complete the Euclidean GCD algorithm with recursion.

DSA Typescript

function gcd(a: number, b: number): number {
  if (b [1] 0) {
    return a;
  }
  return gcd(b, a [2] b);
}

const result = gcd(48, 18);
console.log(result , '');

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

A===

B%

C+

D,

Attempts:

3 left

💡 Hint

Common Mistakes

Using '==' instead of '==='.

Using '+' instead of '%'.

Using '+' instead of ',' in console.log.

The base case checks if b === 0. The recursive call uses a % b. The console.log uses ',' to separate arguments.

Practice

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

easy

A. The difference between the two numbers

B. The Least Common Multiple (LCM)

C. The Greatest Common Divisor (GCD)

D. The sum of the two numbers

Solution

1. Step 1: Understand the Euclidean algorithm purpose

   The Euclidean algorithm is a method to find the greatest common divisor (GCD) of two integers by repeatedly applying division and remainder operations.

2. Step 2: Differentiate GCD from LCM

   While GCD finds the largest number dividing both inputs, LCM finds the smallest number divisible by both. The Euclidean algorithm is specifically for GCD.

3. Final Answer:

   The Greatest Common Divisor (GCD) -> Option C

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

2. Which of the following TypeScript function signatures correctly defines a function to compute GCD using the Euclidean algorithm?

easy

A. function gcd(a: number, b: number): number

B. function gcd(a: string, b: string): string

C. function gcd(a: number): number

D. function gcd(): void

Solution

1. Step 1: Check parameter types for GCD function

   GCD requires two numbers as input, so parameters must be two numbers.

2. Step 2: Check return type

   The function returns a number representing the GCD, so return type must be number.

3. Final Answer:

   function gcd(a: number, b: number): number -> Option A

4. Quick Check:

   Two number inputs and number output [OK]

Hint: GCD needs two number inputs and returns a number [OK]

Common Mistakes:

• Using string types for numeric operations
• Missing one parameter
• Returning void instead of number

3. What is the output of the following TypeScript code?

function gcd(a: number, b: number): number {
  while (b !== 0) {
    const temp = b;
    b = a % b;
    a = temp;
  }
  return a;
}

console.log(gcd(48, 18));

medium

A. 12

B. 3

C. 18

D. 6

Solution

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

   48 % 18 = 12, then gcd(18, 12); 18 % 12 = 6, then gcd(12, 6); 12 % 6 = 0, loop ends, gcd is 6.

2. Step 2: Confirm final returned value

   The function returns 6 after the loop ends.

3. Final Answer:

   6 -> Option D

4. Quick Check:

   GCD(48,18) = 6 [OK]

Hint: Use remainder steps until zero remainder [OK]

Common Mistakes:

• Returning the wrong variable after loop
• Confusing modulo operation
• Stopping too early in the loop

4. Identify the error in this TypeScript function for GCD and fix it:

function gcd(a: number, b: number): number {
  while (a !== 0) {
    const temp = a;
    a = b % a;
    b = temp;
  }
  return b;
}

medium

A. Replace '%' with '/' operator in the loop

B. No error, function works correctly

C. Change 'while (a !== 0)' to 'while (b !== 0)' and swap variables accordingly

D. Change 'return b;' to 'return a;' without other changes

Solution

1. Step 1: Test the function with example inputs

   Trace gcd(48, 18): starts a=48 b=18 -> a=18 b=48 -> a=12 b=18 -> a=6 b=12 -> a=0 b=6, returns 6 (correct GCD).

2. Step 2: Verify algorithm correctness

   This is a valid variant of the Euclidean algorithm with swapped roles (gcd(a,b) = gcd(b % a, a)). No syntax/runtime errors, handles edges like gcd(48,0)=48 correctly.

3. Final Answer:

   No error, function works correctly -> Option B

4. Quick Check:

   Equivalent Euclidean variant computes correct GCD [OK]

Hint: Non-standard loop condition but correct GCD computation [OK]

Common Mistakes:

• Assuming loop must check b !== 0
• Proposing to change return to a (breaks it)
• Suggesting / instead of %

5. Given two numbers 24 and 36, which of the following TypeScript code snippets correctly calculates their Least Common Multiple (LCM) using the GCD function?

hard

A. const lcm = (a: number, b: number): number => (a * b) / gcd(a, b);

B. const lcm = (a: number, b: number): number => gcd(a, b) / (a * b);

C. const lcm = (a: number, b: number): number => a + b - gcd(a, b);

D. const lcm = (a: number, b: number): number => Math.max(a, b);

Solution

1. Step 1: Recall the formula relating LCM and GCD

   LCM(a, b) = (a * b) / GCD(a, b). This formula uses the GCD to find the LCM efficiently.

2. Step 2: Check each code snippet against the formula

   const lcm = (a: number, b: number): number => (a * b) / gcd(a, b); matches the formula exactly. Options B, C, and D do not correctly calculate LCM.

3. Final Answer:

   const lcm = (a: number, b: number): number => (a * b) / gcd(a, b); -> Option A

4. Quick Check:

   LCM = (a*b)/GCD(a,b) [OK]

Hint: LCM = product divided by GCD [OK]

Common Mistakes:

• Dividing GCD by product instead of product by GCD
• Adding or subtracting instead of dividing
• Using max instead of LCM formula