A man is visited by his 7 friends in the following pattern.The first friend visited every day.The second visited every second day.The third visited every third day and so on upto 7th friend on every 7th day.When will they all meet together.

• We need to find the day that is dividable by all friends' intervals. In mathematical terms the solution is the Least Common Multiple of the intervals:
  
  LCM(1,2,3,4,5,6,7)
  
  a simple way to calculate LCM is to factor out each number to products of prime numbers:
  
  1=2^0.3^0.5^0.7^0
  2=2^1.3^0.5^0.7^0
  3=2^0.3^1.5^0.7^0
  4=2^2.3^0.5^0.7^0
  5=2^0.3^0.5^1.7^0
  6=2^1.3^1.5^0.7^0
  7=2^0.3^0.5^0.7^1
  
  then the LCM will be the product of the primes with highest power in each number:
  
  LCM(1,2,3,4,5,6,7) = 2^2.3^1.5^1.7^1 = 4.3.5.7 = 420
  
  Thus they will all meet together in the 420th day.
• 13 years agoHelpfull: Yes(9) No(3)
• LCM(1,2,3,4,5,6,7)= 420 days
• 12 years agoHelpfull: Yes(6) No(1)