# Prime Factorization Homework Problem 2

## Homework Statement

Presidential elections are held every four years. Senators are elected every 6 years. If a senator was elected in the presidential election year of 2000, in what year would he or she campaign again during a presidential election year?

## Homework Equations

dont know how I would show the answer using factorization

2000+6=2006 2000+4=2004+4=2008

## The Attempt at a Solution

2008

symbolipoint
Homework Helper
Gold Member
We need more information on this one. Anyway, try making a table of values starting with year 2000. Again, this seems to be a lowest common factor problem. There is a 4 and a 6, so .... ? ....!

This was all the information I was provided for that question. Do I have the correct answer?

Ok, same caveat (not very good at math), but here's what I think:

2012.

Here's how I arrived at that.

i) Forget the 2000s, they are just confusing. Since it starts at 0, just focus on the 4 and the 6. A president gets elected every 4 years & a senator every 6 years.

ii) Find the lowest (least?) common multiple of 4 and 6 by prime factoring each one.

4 = 2 * 2​
6 = 3 * 2​

iii) Since there are 2s in both groups, circle the largest grouping of 2s (4 = 2*2) and not the other one.

iv) Multiply all the circled prime factors (2*2*3) and you get 12.

v) Draw a chart to check the answer.

Look for their lowest common multiple. And that number is 12.

2000 + 12 = the year 2012