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lcm and gcf

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by resilient » Tue Feb 05, 2008 3:59 pm
I can understand the concept of lcm and gcf by simply drawing out the multipes and seeing where they match.

BUt in the prime factorization way: I get confused on which multiples to eliminate when getting the product of gcf and lcm.

ex. lcm of 18 and 24 - common sense says 72 by looking out at where the mutliples meet. but when seeing harder problems its different you have to look at the prime factors.

18 prime factors are 2,3,3
24 prime factors are 2,2,2,3 and then get the product of the factors. I dont know which factors to eliminate for gcf and lcm. Can someone explain I knew all this but forgot temporarily untill I get your replies.
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by Stuart@KaplanGMAT » Tue Feb 05, 2008 7:45 pm
The lowest common multiple of two numbers has to contain all of the prime factors that each number contains.

24 = 2 * 2 * 2 *3
18 = 2 * 3 * 3

so, we need 2 * 2 * 2 *3 for 24 to go into the number; we already have a 2 and a 3, so for 18 to go into the number we need one more 3.

Therefore, the LCM of 18 and 24 is 2 * 2 * 2 * 3 * 3 = 72
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overlap

by resilient » Tue Feb 05, 2008 8:05 pm
so in order to get lcm I will only use the minimal numbers and no overlap? Is that what this boils down to?
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Re: overlap

by Stuart@KaplanGMAT » Tue Feb 05, 2008 8:13 pm
Enginpasa1 wrote:so in order to get lcm I will only use the minimal numbers and no overlap? Is that what this boils down to?
Correct!
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Re: overlap

by ahsan.saeed » Fri Jan 23, 2009 10:48 pm
Stuart Kovinsky wrote:
Enginpasa1 wrote:so in order to get lcm I will only use the minimal numbers and no overlap? Is that what this boils down to?
Correct!
Hello Stuart,
Can you please solve this question for me, and explain any G.C.F and L.C.M theory behind it? I'm confused about what could be the relationship between the ratio of two numbers and their L.C.M.

I'd really appreciate your response...

Q - The least common multiplier of A and B is 120, the ratio of A and B is 3:4, what is the largest common divisor?
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Re: overlap

by piyush_nitt » Sat Jan 24, 2009 1:53 am
ahsan.saeed wrote:Q - The least common multiplier of A and B is 120, the ratio of A and B is 3:4, what is the largest common divisor?
I am not sure if there is any shorter way but this is how I solved it.

L.C.M = 120

therefore, numbers has to be less than 120 and such that their ratios is 3:4

120 = 2*2*2*3*5

By hit and trail I found out that numbers are 30 and 40

(LCM of 30 and 40 is 120)

G.C.D of 30,40 = 10
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by aroon7 » Sat Jan 24, 2009 7:37 am
Let the numbers be A and B

LCM * GCD = A * B
120 * GCD = 3 (GCD) * 4(GCD)
GCD = 10

is this correct?
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