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?

Answer 1

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

Answer 2

3, right?

Answer 3

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

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

Answer 4

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.

Answer 5

Very good