L1 · FoundationsNumbers & loops~4 min · 6 tests

GCD With the Euclidean Algorithm

Compute the greatest common divisor with Euclid's algorithm in O(log n) instead of trying every divisor. Includes LCM and a speed comparison you can run.

The problem

Return the greatest common divisor of two non-negative integers a and b (not both zero). Don't use math.gcd.

Examples

Example 1
Input
```
gcd(48, 18)
```
Expected output
```
6
```
Example 2
Input
```
gcd(7, 5)
```
Expected output
```
1
```

+ 4 hidden tests on Submit.

Edge cases to ask about

One argument is 0
Equal numbers
Co-prime numbers

Hints

0/3

How an interviewer scores this

0/9

1. Understand the problemRestate it, ask about edge cases and input size.
2. Write a brute-force solutionCorrect first, clever later.
3. Get the correct outputautoAll visible examples pass.
4. Analyse time complexityautoCommit to a Big-O in the Complexity Lab.
5. Analyse space complexityautoExtra memory, not the input.
6. Identify the bottleneckautoMeasure your code — where does it bend?
7. OptimiseUsually: a set or dict instead of a scan.
8. Explain why it worksSay it out loud to Solvi.
9. Test the edge casesautoSubmit passes every hidden test.

Python 3.13 · gcd

def gcd(a, b):
    """Greatest common divisor of a and b."""
    # Write your solution here
    pass

⌘/Ctrl + Enter runs the examples

Your code runs in real CPython inside your browser — nothing is sent anywhere. The first run downloads the interpreter (about 6 MB, once). Your code is saved on this device as you type.

Complexity Lab

What does this cost as n grows?

Interviewers score the analysis as much as the code. Commit to an answer first — then check it, and measure your code against the optimal one at growing input sizes.

Time complexity of the optimal solution

Space complexity (extra memory)

Pick both to reveal the answer.

Measure it

Runs the function on inputs of size 250 up to 16,000 and records the time and peak memory. Slow solutions stop early — a short curve is itself the answer.

From brute force to optimal

The progression an interviewer wants to hear, one step at a time.

Approach	Time	Space	Idea
Try every divisor downwards	O(min(a, b))	O(1)
bestEuclid: gcd(a, b) = gcd(b, a mod b)	O(log min(a, b))	O(1)	The numbers shrink at least by half every two steps.

Walkthrough of the optimal approach (try it yourself first)

Euclid's algorithm: gcd(a, b) = gcd(b, a % b), and gcd(a, 0) = a. The remainders shrink fast — at least halving every two steps — so it is O(log n), against O(n) for trying every divisor.

LCM follows directly: a * b // gcd(a, b).

Complexity: O(log n) time, O(1) space. Each step replaces (a, b) with (b, a mod b), and the remainder at least halves every two steps.

Reveal the reference solution

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

The brute force, for comparison

def gcd(a, b):
    for d in range(min(a, b), 0, -1):
        if a % d == 0 and b % d == 0:
            return d
    return max(a, b)

Follow-ups interviewers ask

LCM of a list of numbers.
Write it recursively.

Frequently asked interview questions

Core interview concepts, complexities, and follow-ups scored by hiring teams.

What is the time complexity of GCD With the Euclidean Algorithm in Python?

The optimal solution runs in O(log n) time and O(1) auxiliary space. Each step replaces (a, b) with (b, a mod b), and the remainder at least halves every two steps.

What is the brute-force approach, and how do you optimise it?

Try every divisor downwards: O(min(a, b)) time, O(1) space. Euclid: gcd(a, b) = gcd(b, a mod b): O(log min(a, b)) time, O(1) space. The numbers shrink at least by half every two steps.

What follow-up questions do interviewers ask about GCD With the Euclidean Algorithm?

LCM of a list of numbers. Write it recursively.