# Greatest common factor, least common multiple.

Discussion in 'Math' started by strantor, Sep 20, 2011.

1. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
5,025
3,107
I'm trying to help my neice with her homework over the internet, via her mom who's also trying to help her. I feel like I'm one of those idiots on "are you smarter than a 5th grader" So, here's what I got (this is the email I am sending her mom, with the homework questions in BOLD, and my answer in italics:

2. ### Papabravo Expert

Feb 24, 2006
12,284
2,723
Brian has 45 tanzas because:
Code ( (Unknown Language)):
1.
2. (4 * 11) +1 = 45 = (9*5)

strantor likes this.
3. ### djsfantasi AAC Fanatic!

Apr 11, 2010
5,464
2,067

Factor 2,700 into it's prime components:
A*B=3*3*3*2*2*5*5

Shuffling terms around using the knowledge we have that 3*5=15 is the greatest common multiple:
A*B=(3*5)*(3*5)*2*2*3
..and introducing our friends x and y from algebra:
A=15*x
B=15*y

...and using the leftover terms,
x*y=2*2*3

This means there are multiple possibilities for the x and y values.
x= 1, 2, 4
y=12, 6, 3

This results in:
A= 15, 30, 60
B=180, 90, 45

Now using the three possible sets for x and y, I come up with three different answers, depending on which of the three perfectly valid choices we make for the 2 numbers whcih multiply together to get 2,700:
A= 3*5 =15
B= 2*2*3*3*5 =180
Least common multiple =2*2*3*3*5 =180

A= 2*3*5 =30
B= 2*2*3*5*5 =90
Least common multiple =2*2*3*5*5 =90

A= 2*2*3*5 =60
B= 3*3*5 =45
Least common multiple =2*2*3*3*5 =180

Your neice probably needs one correct answer. I like A=30 and B=90 because it stared me right in the face. In fact, I almost convinced myself it was the only answer.

4. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
5,025
3,107
@djsfantasi
I thought it was going to be a lot simpler than that. I think this stuff is supposed to be pre-algebra. Thanks for the answer, I will let her know.

5. ### Zazoo Member

Jul 27, 2011
114
43
One correction, of the remaining factors of 2*2*3 the pair of twos must remain in A or B, if you put a single two in both A and B then the GCF becomes 30 not 15. So the second one won't satisfy the required GCF

Last edited: Sep 20, 2011
djsfantasi likes this.
6. ### Georacer Moderator

Nov 25, 2009
5,154
1,281
What's a tanza anyway?

I 'd like to justify Papabravo's answer:

We know that:
$11 \cdot N +1 =9 \cdot K \text{, where }N,K \in \mathbb{N} \Leftrightarrow
K=\frac{11 \cdot N +1}{9}$

The first N that makes K an integer is N=4 and K=5

strantor likes this.
7. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
5,025
3,107
No idea. it's something they have in the philippines I guess (that's where my neice is)