Can you explain how to do this question? "Three clocks ring once at the same time. After that, the first clock rings after every 90 minutes, the second after every 30 minutes, and third after every 60 minutes. After how many minutes will they again ring together?

Use prime number division to determine the Least Common Denominator:

30 = 2 x 3 x 5
60 = 2 x 2 x 3 x 5
90 = 2 x 3 x 3 x 5

Now write each term the maximum number of times it appears in each equation: 2 appears twice in the 60 minute equation, 3 appears twice in the 90 minute equation, and 5 appears only once in all three equations.

2 x 2 x 3 x 3 x 5 = 180 minutes

And that's your answer.

What is the least common multiple of 90, 30, and 60?

3, right?

No. 3 isn't even the lowest common factor.

What is the smallest number that can be evenly divided by 30, 60, and 90?

Very good

To solve this question, we need to find the least common multiple (LCM) of the three given time intervals - 90 minutes, 30 minutes, and 60 minutes. The LCM represents the smallest common multiple of the three numbers.

To find the LCM, we can follow these steps:

Step 1: List the multiples of each given time interval until we find a common multiple.
- For the first clock, the time interval is 90 minutes. The multiples would be 90, 180, 270, 360, 450, 540, and so on.
- For the second clock, the time interval is 30 minutes. The multiples would be 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, and so on.
- For the third clock, the time interval is 60 minutes. The multiples would be 60, 120, 180, 240, 300, 360, 420, 480, 540, and so on.

Step 2: Identify the smallest number that appears in all three lists. In this case, the smallest number that appears in all three lists is 180 minutes.

Therefore, the clocks will again ring together after 180 minutes.