posted by carl .
Venus begins a new year every 225 days. Earth begins a new year every 365 days. If both planets begin a new year on the same day, how many days will pass befor that happens again.
Think of the problem of two runners around a 1-kilometer track. Runner A can make one round in 8 minutes, and runner B can do this in 6 minutes. If they start together, when will they meet at the starting point again?
2 | 8, 6
| 4, 3
Take the LCM of 8 and 6 to get 24. Runner A would have done 3 laps, while B would have done 4.
The LCM of 225 and 365 can be found in different ways. One way is to find the factors, and eliminate one of the common factors, the other is to do a simple division. Since the numbers are quite large, we will try the second way. The first number is a common divisor, and the second and third are the original numbers.
5 | 225 365 (divide 225 to get 45, etc)
Since there are no more common factors, the LCM is 5*45*73, the number of days when Earth and Venus have the new years on the same day again.