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# What is the range for the Least common multiple for 15, 18,

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Intern
Joined: 22 Sep 2004
Posts: 28
What is the range for the Least common multiple for 15, 18, [#permalink]

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05 Sep 2007, 16:03
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What is the range for the Least common multiple for 15, 18, 40 ,50?

VP
Joined: 08 Jun 2005
Posts: 1145

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05 Sep 2007, 16:37
LCM[15,18,40,50]

15 = 5*3
18 = 3*2*3
40 = 2*2*2*5
50 = 5*2*5

so the Least Common Multiple is 5*3*2*2*2*5*3 = 100*18 = 1,800

Director
Joined: 12 Jun 2006
Posts: 532

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05 Sep 2007, 19:48
What made you multiply certain prime #s together to get the answer?
CEO
Joined: 29 Mar 2007
Posts: 2559
Re: PS-the Least common multiple [#permalink]

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05 Sep 2007, 21:47
ttar wrote:
What is the range for the Least common multiple for 15, 18, 40 ,50?

Can someone clarify why its asking "the range" for the LCM this is confusing me.

They are using primes b/c to find the LCM you

First find the primes of each number:

15: 5,3. 18: 3,3,2. 40: 2,2,2,5 50: 2,5,5.

Now find the product of all the primes USING THE HIGHER POWER of the repeated prime.

For example: 40 has the most 2's so we use its 3 2's and only its 3 2's to find the LCM. Do the same for the other numbers.

2*2*2*3*3*5*5 --> 8*9*25--> 72*25---> 1800.
Manager
Joined: 10 Aug 2007
Posts: 63
Re: PS-the Least common multiple [#permalink]

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05 Sep 2007, 23:51
GMATBLACKBELT wrote:
ttar wrote:
What is the range for the Least common multiple for 15, 18, 40 ,50?

Can someone clarify why its asking "the range" for the LCM this is confusing me.

They are using primes b/c to find the LCM you

First find the primes of each number:

15: 5,3. 18: 3,3,2. 40: 2,2,2,5 50: 2,5,5.

Now find the product of all the primes USING THE HIGHER POWER of the repeated prime.

For example: 40 has the most 2's so we use its 3 2's and only its 3 2's to find the LCM. Do the same for the other numbers.

2*2*2*3*3*5*5 --> 8*9*25--> 72*25---> 1800.

GMATBLACKBELT, according to what you said, can you please explain me why the following does not hold?

Consider the numbers 98, 14 and 20.
98 = 49*2 = 7*7*2
14 = 7*2
20 = 2*2*5

Then the least common multiple should be (7*7)*(2*2) = 196, which is not a factor of 20.

Have I misunderstood you or is there something missing in your statement? I would really appreciate your feedback.
Manager
Joined: 10 Aug 2007
Posts: 63

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05 Sep 2007, 23:55
To add to my previous thinking I beleive that the LCD of 98, 14 and 20 is 490. I don't see how you can reach this result be multiplying using the higher powers of teh repeated primes.
VP
Joined: 08 Jun 2005
Posts: 1145

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06 Sep 2007, 03:32
after15 wrote:
To add to my previous thinking I beleive that the LCD of 98, 14 and 20 is 490. I don't see how you can reach this result be multiplying using the higher powers of teh repeated primes.

LCM[98,14,20]

98 = 7*7*2

14 = 2*7

20 = 2*5*2

LCM = 7*7*2*2*5 = 980

you forgot to count the five !

Last edited by KillerSquirrel on 06 Sep 2007, 09:46, edited 2 times in total.
Manager
Joined: 10 Aug 2007
Posts: 63

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06 Sep 2007, 04:48
Ok, maybe I'm retarded or something but I still do not get it. According to what is mentioned in the previous posts regarding this thread, I should multiply the higher powers of the repeated primes.

KillerSquirrel, I do not get you

98 = 7*7*2. I guess the repeated primes here are 7*7
14 = 2*7. No repeated primes here.
20 = 2*2*5. Repeated numbers are 2*2 but they are not primes...

How can you say then that LCM = 7*7*2*5 ??

Now I'm even more confused
VP
Joined: 08 Jun 2005
Posts: 1145

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06 Sep 2007, 07:57
after15 wrote:
Ok, maybe I'm retarded or something but I still do not get it. According to what is mentioned in the previous posts regarding this thread, I should multiply the higher powers of the repeated primes.

KillerSquirrel, I do not get you

98 = 7*7*2. I guess the repeated primes here are 7*7
14 = 2*7. No repeated primes here.
20 = 2*2*5. Repeated numbers are 2*2 but they are not primes...

How can you say then that LCM = 7*7*2*5 ??

Now I'm even more confused

Don't be !

LCM
---
The least common multiple of two (or more) numbers is the product of
one number times the factors of the other number(s) that aren't
common.

If you wanted to find the least common multiple of 32 and 76, you'd
multiply 32 by 19, because 19 is the only factor of 76 that isn't
common to the factors of 32.

In the same way the least common multiple of 98,14,20 = 98*5*2 = 980

Last edited by KillerSquirrel on 06 Sep 2007, 09:47, edited 1 time in total.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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06 Sep 2007, 08:12
ggarr wrote:
What made you multiply certain prime #s together to get the answer?

I'm sorry. I couldn't think of a good way to explain, but I think killersquirrel has done a good job with the explanation.
Manager
Joined: 10 Aug 2007
Posts: 63

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06 Sep 2007, 09:41
KillerSquirrel I get what you said and I would like to thank you for your explanation. I have a last question however.

As you explained before, we must use the higher power of the repeated primes:

98 = 7*7*2
20 = 2*2*5
14 = 2*7

Ok. Prime number 7 appears in 98 2 times (higher power). Prime number 2 appears twice in 20 (higher power).

Why then LCD is not 7*7*2*2*5? Why do not we multiply 2*2 and instead only once? Isn't it the higher repeated power? I know that this gives a result of 980, which is wrong, but why does the rule not work here? It works on all the other examples in this thread.

I hope it is too annoying for you. In that case I apologize anyway.
VP
Joined: 08 Jun 2005
Posts: 1145

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06 Sep 2007, 10:03
after15 wrote:
KillerSquirrel I get what you said and I would like to thank you for your explanation. I have a last question however.

As you explained before, we must use the higher power of the repeated primes:

98 = 7*7*2
20 = 2*2*5
14 = 2*7

Ok. Prime number 7 appears in 98 2 times (higher power). Prime number 2 appears twice in 20 (higher power).

Why then LCD is not 7*7*2*2*5? Why do not we multiply 2*2 and instead only once? Isn't it the higher repeated power? I know that this gives a result of 980, which is wrong, but why does the rule not work here? It works on all the other examples in this thread.

I hope it is too annoying for you. In that case I apologize anyway.

You are correct ! the LCM is indeed 980 not 490 - my posts have been corrected.

VP
Joined: 08 Jun 2005
Posts: 1145

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06 Sep 2007, 10:25
IrinaOK wrote:
KillerSquirrel wrote:
LCM[15,18,40,50]

15 = 5*3
18 = 3*2*3
40 = 2*2*2*5
50 = 5*2*5

so the Least Common Multiple is 5*3*2*2*2*5*3 = 100*18 = 1,800

ttar,

The question says "range of..." is that typo, or is it how the questions would be correctly stated?
the wording is a bit confusing here, plzz answer.

I also got confused by the word "range". I chose to ignore it.

Manager
Joined: 10 Aug 2007
Posts: 63

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06 Sep 2007, 10:46
Thank you very much KillerSquirrel for your help and your overall attitude. You have been really helpful+supportive. I really apreciate it.
06 Sep 2007, 10:46
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