# Prime Factorization Homework Problem 1

## Homework Statement

Margo has piano lessons every two weeks. Her brother Roberto has a soccer tournament every three weeks. Her sister Randa has an orthodontist appointment every four weeks. If they all have activities this Friday, how long will it be before all of their activities fall on the same day again?

## Homework Equations

Factored 2, 3, and 4

## The Attempt at a Solution

6 weeks

symbolipoint
Homework Helper
Gold Member
Try literally making a table or chart. The description you gave seems to suggest to look for the lowest common multiple.

Chart making would take time, I think. I think this can be also solve by the solution I just mentioned. Like 1/2, 1/3, 1/4. And 1/(sum of the 1/2, 1/3, 1/4), and the answer is 0.9. As the answer is larger than 1/4(once a four week)which is 0.25, I think you got the right answer, but I don't know...Sorry :^(

Thanks!

I'm not one to be trusted in math, but I think the answer is 12 weeks.

Here's how I got that:

Frequencies = 1/2 ; 1/3 ; 1/4

Least (Lowest) Common Multiple - 12

How I arrived at 12 (i.e., factoring the denominators)

1/2 = 2
1/3 = 3
1/4 = 2 * 2

Since the twos repeat, take only the biggest group of prime factored twos (the 2 * 2 from the 1/4) and take the 3. Multiply them together 2 * 2 * 3 = 12.

12 = LCM, t/f 12 weeks from now.

(Then I drew out a chart and checked it & it seemed to work out correctly).

It can't be six weeks because Randa's appointment is every 4 weeks and that does not work.

I didn't really bother doing any calculations but let's make a little table anyway.

Margo has lessons every 2 weeks: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Boberto has soccer every 3 weeks: 3, 6, 9, 12, 15, 18
Randa has an appointment every 4 weeks: 4, 8, 12, 16, 20

As you can see, the lowest common multiple is 12 and not 6. I'm also not the one to be trusted in math but I think that's the answer you're looking for.