Problem
Solution
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Find the LCM (Least Common Multiple) of Two Numbers
Certification: Basic Level
Accuracy: 69.77%
Submissions: 43
Points: 5
Write a Python program that calculates the Least Common Multiple (LCM) of two positive integers.
Example 1
- Input: a = 12, b = 15
- Output: 60
- Explanation:
- Step 1: Find the greatest common divisor (GCD) of 12 and 15, which is 3.
- Step 2: Calculate LCM using the formula: LCM(a,b) = (a * b) / GCD(a,b)
- Step 3: LCM = (12 * 15) / 3 = 180 / 3 = 60
- Step 4: Return 60 as the LCM.
Example 2
- Input: a = 7, b = 9
- Output: 63
- Explanation:
- Step 1: Find the greatest common divisor (GCD) of 7 and 9, which is 1.
- Step 2: Calculate LCM using the formula: LCM(a,b) = (a * b) / GCD(a,b)
- Step 3: LCM = (7 * 9) / 1 = 63 / 1 = 63
- Step 4: Return 63 as the LCM.
Constraints
- 1 ≤ a, b ≤ 10^6
- Time Complexity: O(log(min(a, b))) for the GCD calculation
- Space Complexity: O(1) as no additional space is needed
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Solution Hints
- Use formula: LCM(a, b) = (a * b) / GCD(a, b)
- Find GCD first, then compute LCM
- Avoid overflow by using: LCM(a, b) = (a // gcd(a, b)) * b