LCM using Recursion
Detailed guide and Python implementation for the 'LCM using Recursion' problem.
Problem Statement
Write a function lcm(a, b) that computes the Least Common Multiple (LCM) of two positive integers a and b using recursion. Use the relationship: LCM(a, b) = (a * b) // HCF(a, b). Implement the HCF helper using recursion as well.
- •1 <= a, b <= 10^6
Examples
a = 4, b = 6
12
HCF(4,6) = 2. LCM = (4*6) // 2 = 12. The multiples of 4 are 4,8,12,... and multiples of 6 are 6,12,... The smallest common is 12.
a = 12, b = 15
60
HCF(12,15) = 3. LCM = (12*15) // 3 = 60.
a = 7, b = 3
21
HCF(7,3) = 1. LCM = (7*3) // 1 = 21.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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