Anita owns a beauty supply store. Every two weeks she receives a supply of shampoo. Every four weeks she receives a carton of nail polishes. Every eight weeks she receives a box of combs, and every twelve weeks she receives a box of hair dyes. If Anita received a shipment of all these supplies today, when is the next time all four supplies will arrive on the same day?

that would be correct.

To find the next time all four supplies will arrive on the same day, we need to find the least common multiple (LCM) of the time intervals for each supply.

The time intervals for each supply are as follows:
- Shampoo: every 2 weeks
- Nail polishes: every 4 weeks
- Combs: every 8 weeks
- Hair dyes: every 12 weeks

Let's find the LCM of these intervals step by step:

Step 1: Find the LCM of 2 and 4.
The multiples of 2 are: 2, 4, 6, 8, ...
The multiples of 4 are: 4, 8, 12, 16, ...
The LCM of 2 and 4 is 4, since it is the smallest number that is a common multiple of both 2 and 4.

Step 2: Find the LCM of the result from step 1, which is 4, and 8.
The multiples of 4 are: 4, 8, 12, 16, ...
The multiples of 8 are: 8, 16, 24, 32, ...
The LCM of 4 and 8 is 8, since it is the smallest number that is a common multiple of both 4 and 8.

Step 3: Find the LCM of the result from step 2, which is 8, and 12.
The multiples of 8 are: 8, 16, 24, 32, ...
The multiples of 12 are: 12, 24, 36, 48, ...
The LCM of 8 and 12 is 24, since it is the smallest number that is a common multiple of both 8 and 12.

Therefore, the next time all four supplies will arrive on the same day is in 24 weeks.

well, what is the smallest number which is a multiple of 2,4,8 and 12?

Is it 24?