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The least common multiplier of A and B is 120, the ratio of [#permalink]

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09 Jan 2009, 19:52

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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?

Can someone break this down step by step for me ? I find that Im having some difficulty in understanding the concept behind these types of questions. Thanks in advance

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?

Can someone break this down step by step for me ? I find that Im having some difficulty in understanding the concept behind these types of questions. Thanks in advance

Given LCM = 120 and the ratio of the numbers = 3:4. We need to find the GCD.

Let the numbers be 3x and 4x. So it is clear that their GCD = x.

We have,

\(LCM \times GCD = Product \quad of \quad the \quad two \quad numbers\)

\(\Rightarrow 120 \times x = 3x \times 4x\)

\(\Rightarrow x = 10\)

Hence the greatest common divisor is 10
_________________

I'm not sure if anybody's still interested in this question, but I found the solutions posted earlier a bit tedious to think up in under two minutes. This got me thinking a bit more deeper into what the question's actually telling; and here's how I reasoned an answer:

Given: LCM (A,B) = 120 That bit's telling that for the two numbers A and B:

The [Common multiples between (A,B)] x [Uncommon multiples between them] = 120 That's the wordy definition of LCM right? Take out all that's common, and multiply them with whatever uncommon remains and you'll get the LCM between A and B

Now, what's worth noting in this equation is that the first part of it [Common multiples (A,B)] is simply their GCF; So, 120 = GCF (A,B) x [Uncommon Factors of (A,B)]

I got this far in my thought process, and then gave up, because I thought there wasn't any information on what's uncommon between A,B.. But wait! The question says that A/B = 3/4 ... that's as good as saying that 3 and 4 are the only factors that would remain if I divided A and B -- 3 and 4 are the Uncommon factors between A and B

So, using this bit of information, now you can solve for the GCF:

120 = GCF (A,B) x 3 x 4 120 = GCF x 12 GCF = 10

From this I realized something really simple but which was not obvious to me:

LCM / GCF = product of uncommon factors; if you are given the ratio between the numbers, then each value in the ratio is an uncommon factor belongs to one of the numbers [i.e if two numbers are in the ratio 15:16, then their GCFx15x16 would give you their LCM]

Hope that helps! Raj

ps: excuse me if you find any errors/ if i am not clear, but as you may notice below my username, this is my first post!

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?

Can someone break this down step by step for me ? I find that Im having some difficulty in understanding the concept behind these types of questions. Thanks in advance

Given LCM = 120 and the ratio of the numbers = 3:4. We need to find the GCD.

Let the numbers be 3x and 4x. So it is clear that their GCD = x.

We have,

\(LCM \times GCD = Product \quad of \quad the \quad two \quad numbers\)

\(\Rightarrow 120 \times x = 3x \times 4x\)

\(\Rightarrow x = 10\)

Hence the greatest common divisor is 10

Yup, I got there the same way.

Thanks for a smart and efficient way!

+1 , Thats indeed a smart way . A concept can be used to solve this problem- When you say LCM of A and B (for example A=3 and B=4 ) then we know for sure that the LCM of A and B (which is 120 here) will be divisible by both A and B ,that give us no1= 120/A=120/3= 40 & no2= 120/B=120/4 =30

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?

Can someone break this down step by step for me ? I find that Im having some difficulty in understanding the concept behind these types of questions. Thanks in advance

This can be solved using the principal of LCM X HCF = Product of the numbers.

LCM = 120

Ratio is 3:4. So let the numbers be 3x and 4x. Now, when we multiply numerator and denominator with x , the variable x becomes the HCF, thinking logically. Because cancelling the greatest factor we turn up to 3:4 which cannot be simplified further.

So finally we have

3x*4x = x*120 which gives x = 10. Ans : 10
_________________

GMAT done - a mediocre score but I still have a lot of grit in me

Re: The least common multiplier of A and B is 120, the ratio of [#permalink]

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03 Oct 2013, 18:29

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Re: The least common multiplier of A and B is 120, the ratio of [#permalink]

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10 Nov 2014, 22:36

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Re: The least common multiplier of A and B is 120, the ratio of [#permalink]

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28 Nov 2015, 12:39

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Re: The least common multiplier of A and B is 120, the ratio of [#permalink]

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19 Feb 2017, 03:10

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