import sys
import math
from lxml import etree

def calculate_lcm(a, b):
    return abs(a * b) // math.gcd(a, b)

def main(input_file):
    try:
        tree = etree.parse(input_file)
    except FileNotFoundError:
        print(f"Error: Input file '{input_file}' not found.")
        sys.exit(1)
    except etree.ParseError:
        print(f"Error: Failed to parse the XML file '{input_file}'.")
        sys.exit(1)

    root = tree.getroot()
    non_zero_values = []

    for period_element in root.xpath("//period"):
        period_value = int(period_element.text)
        if period_value != 0:
            non_zero_values.append(period_value)

    if not non_zero_values:
        print("No non-zero values found in the XML file.")
    else:
        #print ("Periods: " + str (non_zero_values));
        lcm = non_zero_values[0]
        for value in non_zero_values[1:]:
            lcm = calculate_lcm(lcm, value)

        feas = lcm * 2
        print(feas)

if __name__ == "__main__":
    if len(sys.argv) != 2:
        print("Usage: python script.py input_file.xmlv3")
        sys.exit(1)

    input_file = sys.argv[1]
    main(input_file)