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# Greatest Common Factor and Least Common Multiple

Wow. I made a really stupid mistake. That's embarrassing.

Spoiler for Ok, I think I finally got it

Go to the full post

8 replies to this topic

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Posted 29 July 2013 - 04:36 AM

A while ago, I gave my Pre-algebra class a puzzle problem: "Given two natural numbers,  m and n. If their GCD is G=6 and their LCM is L=72, what are the numbers?"

a) What were all possible (m, n) for G=6 and L=72 (m<=n)?
b) What's the smallest sum, m+n, for any (m, n) pair that share the same G=gcd and L=lcm (with another m<=n; G>=2)?
c) Find the (G, L) pair with the most solutions (m, n) for the same G=gcd(m,n) and L=lcm(m,n) (G>1, L < 1001).

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### #2 gavinksong

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Posted 29 July 2013 - 05:15 AM

Edited by gavinksong, 29 July 2013 - 05:18 AM.

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### #3 DeGe

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Posted 29 July 2013 - 10:27 AM

Spoiler for For b

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### #4 gavinksong

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Posted 29 July 2013 - 03:50 PM

Spoiler for For b

It says G >= 2.

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Posted 29 July 2013 - 03:57 PM

for B, of pairs of whole numbers, what is the smallest m+n where (m,n) and (p,q) have the same lcd and gcf?

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### #6 gavinksong

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Posted 29 July 2013 - 05:07 PM

for B, of pairs of whole numbers, what is the smallest m+n where (m,n) and (p,q) have the same lcd and gcf?

Oh, I see. So DeGe pretty much had it.

Spoiler for except

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Posted 29 July 2013 - 06:48 PM

for B, of pairs of whole numbers, what is the smallest m+n where (m,n) and (p,q) have the same lcd and gcf?

Oh, I see. So DeGe pretty much had it.
Spoiler for except

M, n, p, and q are distinct
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### #8 gavinksong

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Posted 29 July 2013 - 07:17 PM

Wow. I made a really stupid mistake. That's embarrassing.

Spoiler for Ok, I think I finally got it

• 0

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Posted 29 July 2013 - 08:25 PM   Best Answer

Wow. I made a really stupid mistake. That's embarrassing.

Spoiler for Ok, I think I finally got it