Least Common Multiple

Problem

Return the least common multiple of a and b, the smallest positive number that both divide. lcm(a, b) = a / gcd(a, b) × b.

Implement lcm(a, b).

a: The first positive number. b: The second positive number.

Return lcm(a, b).

1 ≤ a, b ≤ 1,000,000,000

Example 1

Input:
a = 4
b = 6

Expected output:
expected = 12

Input:
long long a = 4;
long long b = 6;

Expected output:
long long expected = 12;

Input:
long a = 4;
long b = 6;

Expected output:
long expected = 12;

Multiples of 4: 4, 8, 12…; multiples of 6: 6, 12…; the first common one is 12.

Example 2

Input:
a = 7
b = 7

Expected output:
expected = 7

Input:
long long a = 7;
long long b = 7;

Expected output:
long long expected = 7;

Input:
long a = 7;
long b = 7;

Expected output:
long expected = 7;

A number's LCM with itself is the number: 7.

Try on your own first, then open one hint at a time.

Hint 1

Use the relationship between gcd and lcm instead of searching for multiples.

Hint 2

Compute the gcd first, then combine the two numbers carefully.

Hint 3

Divide before multiplying to reduce overflow risk, even with large inputs.

Expected complexity

O(log min(a, b)) time, O(1) extra space

This challenge is adapted for CodeUtility. Follow the statement and constraints above.