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# Having issues with finding LCM and GCF, can someone help?

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Manager
Joined: 25 Jul 2012
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Having issues with finding LCM and GCF, can someone help? [#permalink]

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09 Feb 2013, 11:07
Hello all,

I have been prepping with the almighty MGMAT books, which are great. However, divisibility is being a pain. It's mostly just finding the methods on how to find the the GCF and LCM. I really don't care for MGMAT's venn diagram method. Can someone teach me how to do get these more efficiently using my method? Also does anyone have any drill type of problems for these? Doing drills helps me learn the most.

My method:

Here's my method for two integers which is not so hard for me:

What is the GCF and LCM of 420 and 660?

1. Break down into primes (easy and fast for me)

420: 2 x 2 x 3 x 5 x 7
660: 2 x 2 x 3 x 5 x 11

2. find GCF and LCM:

GCF (I get this): multiply common primes: 2 x 2 x 3 x 5 = 11

LCM (I like crossing out numbers from the primes list above, but maybe I shouldn't do this): So I cross out 2 x 2 x 3 x 5 prom primes list and then multiply 2 x 2 x 3 x 5 x 7 x 11 = 4,620

---------

Three integers - this is where I get stuck sometimes:

What is the GCF and LCM of 100, 140 and 250?

1. Primes (easy part)

100: 2 x 2 x 5 x 5
140: 2 x 2 x 5 x 7
250: 2 x 5 x 5 x 5

2. Find LCM and GCF

GCF: (all share 2 and 5) 2 x 5 = 10
LCM: This is where I get stuck, I don't how to cross out my numbers here? Answer is 3500
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Re: Having issues with finding LCM and GCF, can someone help? [#permalink]

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09 Feb 2013, 11:57
1
KUDOS
Expert's post
For LCM find the largest combination for each prime number:

100: 2 x 2 x 5 x 5
140: 2 x 2 x 5 x 7
250: 2 x 5 x 5 x 5

So, 100 (or 140) has the largest number of 2 (2 x 2)
140 has the largest number of 7 (7)
250 has the largets number of 5 (5 x 5 x 5)

LCM = 2 x 2 x 7 x 5 x 5 x 5 = 3500

DelSingh wrote:
...What is the GCF and LCM of 100, 140 and 250?

1. Primes (easy part)

100: 2 x 2 x 5 x 5
140: 2 x 2 x 5 x 7
250: 2 x 5 x 5 x 5

2. Find LCM and GCF

GCF: (all share 2 and 5) 2 x 5 = 10
LCM: This is where I get stuck, I don't how to cross out my numbers here? Answer is 3500

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Manager
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Location: United States
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Re: Having issues with finding LCM and GCF, can someone help? [#permalink]

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09 Feb 2013, 13:48
walker wrote:
find the largest combination for each prime number

Perfectly said, those words sound angelic... It makes sense now. I was sort of thinking backwards in my head in order to come with the LCM. Thanks man!
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Re: Having issues with finding LCM and GCF, can someone help? [#permalink]

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25 Jun 2014, 06:58
I had a similar issue with LCM and try to remember that after expressing the terms of prime factors, the LCM is the product of the primes with the highest powers of all the factors

For LCM find the largest combination for each prime number:

100: 2 x 2 x 5 x 5 = $$2^2 * 5^2$$
140: 2 x 2 x 5 x 7 = $$2^2 * 5 * 7$$
250: 2 x 5 x 5 x 5 = $$2 * 5^3$$

LCM=$$2^2 * 5^3 * 7$$
LCM=4 * 125 * 7
LCM= 500*7
LCM=3500
Re: Having issues with finding LCM and GCF, can someone help?   [#permalink] 25 Jun 2014, 06:58
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