# There has just been a planetary alignment of five planets in the system Blogg, all the astrologers have gone loopy, and they want to know when the next occurance of these five planets will happen again.

Krypton the nearest planet to the sun takes 6 days to orbit the sun.

Zenon the next planet takes 23 days to orbit the sun.

Argon the middle planet take 37 days.

Neon the largest planet takes 68 days.

And Radon the last planet take 137 days to orbit the sun.

25000 + 1200

show your work

its wrong anyways :/

The answer is 23,783,748 days. There will certainly be an alignment after

6 X 23 X 37 X 68 X 137 = 47,567,496 days. However, the first alignment

will occur after the smallest number of days that can be divided by 6,

23, 37, 68, and 137 to give an integer. To find this numer, we look at the

factors of all of these numbers: 23, 37, and 137 are prime, 6 = 2 X 3,

and 68 = 2 X 2 X 17. Thus we need 2 X 2 X 3 X 17 X 23 X 37 X 137 =

23,783,748 days.

The answer is 23,783,748 days. There will certainly be an alignment after

6 X 23 X 37 X 68 X 137 = 47,567,496 days. However, the first alignment

will occur after the smallest number of days that can be divided by 6,

23, 37, 68, and 137 to give an integer. To find this numer, we look at the

factors of all of these numbers: 23, 37, and 137 are prime, 6 = 2 X 3,

and 68 = 2 X 2 X 17. Thus we need 2 X 2 X 3 X 17 X 23 X 37 X 137 =

23,783,748 days.

## To determine when the next planetary alignment of these five planets will occur, we need to find the smallest number of days that is divisible by the orbital period of each planet.

Krypton takes 6 days to complete one orbit around the sun.

Zenon takes 23 days.

Argon takes 37 days.

Neon takes 68 days.

And Radon takes 137 days.

To find the smallest number of days that can be divided evenly by these five values, we need to find the least common multiple (LCM) of 6, 23, 37, 68, and 137.

First, let's break down each number into its prime factors:

6 = 2 x 3

23, 37, and 137 are prime numbers themselves.

68 = 2 x 2 x 17

Now, we can find the LCM by taking the highest power of each prime factor:

2 x 2 x 3 x 17 x 23 x 37 x 137

Calculating this gives us:

23,783,748 days

Therefore, the next occurrence of the alignment of these five planets in the system Blogg will happen after 23,783,748 days.