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44 lines
904 B
Python
44 lines
904 B
Python
"""
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Problem:
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2520 is the smallest number that can be divided by each of the numbers from 1
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to 10 without any remainder.
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What is the smallest positive number that is evenly divisible(divisible with no
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remainder) by all of the numbers from 1 to N?
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"""
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""" Euclidean GCD Algorithm """
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def gcd(x, y):
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return x if y == 0 else gcd(y, x % y)
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""" Using the property lcm*gcd of two numbers = product of them """
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def lcm(x, y):
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return (x * y) // gcd(x, y)
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def solution(n):
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"""Returns the smallest positive number that is evenly divisible(divisible
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with no remainder) by all of the numbers from 1 to n.
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>>> solution(10)
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2520
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>>> solution(15)
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360360
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>>> solution(20)
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232792560
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>>> solution(22)
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232792560
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"""
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g = 1
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for i in range(1, n + 1):
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g = lcm(g, i)
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return g
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if __name__ == "__main__":
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print(solution(int(input().strip())))
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