# Kurt-Werles-MacBook-Pro:/Users/kurt% ruby lcm_math.rb 5 6 7 10
# 5/6 * 5/5 = 25/30
#
# 7/10 * 3/3 = 21/30
#
# 25/30 + 21/30 = 46/30

numerator_a = ARGV[0].to_i
denominator_a = ARGV[1].to_i
numerator_b = ARGV[2].to_i
denominator_b = ARGV[3].to_i

lcm = denominator_a.lcm(denominator_b)
multiplier_a = lcm / denominator_a
multiplier_b = lcm / denominator_b

numerator_a_prime = numerator_a * multiplier_a
denominator_a_prime = denominator_a * multiplier_a

numerator_b_prime = numerator_b * multiplier_b
denominator_b_prime = denominator_b * multiplier_b # which had better be the same as denominator_a_prime

puts “#{numerator_a}/#{denominator_a} * #{multiplier_a}/#{multiplier_a} = #{numerator_a_prime}/#{denominator_a_prime}”

puts “”

puts “#{numerator_b}/#{denominator_b} * #{multiplier_b}/#{multiplier_b} = #{numerator_b_prime}/#{denominator_b_prime}”

puts “”

puts “#{numerator_a_prime}/#{denominator_a_prime} + #{numerator_b_prime}/#{denominator_b_prime} = #{numerator_a_prime + numerator_b_prime}/#{denominator_b_prime}”

# I love ruby. lcm. Who knew?