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.

you are finding the LCM of 225 and 365

225 = 5x5x3x3
365 = 5x73

LCM = 5x5x3x3x73 = 16425 days

To find out how many days will pass before Venus and Earth begin a new year on the same day again, we need to determine the least common multiple (LCM) of their respective orbital periods.

The orbital period of Venus is 225 days, and the orbital period of Earth is 365 days.

To find the LCM, we can list out the multiples of each number until we find the next common multiple:

Multiples of 225: 225, 450, 675, 900, 1125, 1350, 1575, 1800, ...
Multiples of 365: 365, 730, 1095, 1460, 1825, 2190, 2555, 2920, ...

Looking at the lists, we can see that the first common multiple is 2920.

Therefore, it takes 2920 days for Venus and Earth to begin a new year on the same day again.