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How do you compute the GCD of two numbers?

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01

Understand the problem

Explain Euclid's algorithm.

mathgcd
02

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03

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Euclid's algorithm: gcd(a, b) = gcd(b, a % b) until b is 0, then a is the GCD. It runs in O(log min(a,b)). The LCM is then a*b / gcd(a,b).

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04

Read the code

Euclid's algorithm + LCM
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def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def lcm(a, b):
    return a // gcd(a, b) * b      # divide first to avoid overflow


# --- demo ---  (stdlib: math.gcd, math.lcm)
print(gcd(48, 18))   # 6
print(lcm(4, 6))     # 12
05

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