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If A is the smallest positive integer that is divisible by all the int

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If A is the smallest positive integer that is divisible by all the int  [#permalink]

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New post 05 Sep 2018, 13:08
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If A is the smallest positive integer that is divisible by all the integers between 24 and 27, inclusive, and B is the smallest positive integer that is divisible by all the integers between 15 and 18, inclusive, the greatest positive number that divides both A and B completely is

A. 360
B. 720
C. 2160
D. 4320
E. 6480

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Re: If A is the smallest positive integer that is divisible by all the int  [#permalink]

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New post 05 Sep 2018, 13:45
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GmatDaddy wrote:
If A is the smallest positive integer that is divisible by all the integers between 24 and 27, inclusive, and B is the smallest positive integer that is divisible by all the integers between 15 and 18, inclusive, the greatest positive number that divides both A and B completely is

A. 360
B. 720
C. 2160
D. 4320
E. 6480


We have to find out, HCF(LCM(24,25,26,27),LCM(15,16,17,18))=HCF(70200,12240)=360

Ans. (A)
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Re: If A is the smallest positive integer that is divisible by all the int  [#permalink]

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New post 05 Sep 2018, 18:28
PKN wrote:
GmatDaddy wrote:
If A is the smallest positive integer that is divisible by all the integers between 24 and 27, inclusive, and B is the smallest positive integer that is divisible by all the integers between 15 and 18, inclusive, the greatest positive number that divides both A and B completely is

A. 360
B. 720
C. 2160
D. 4320
E. 6480


We have to find out, HCF(LCM(24,25,26,27),LCM(15,16,17,18))=HCF(70200,12240)=360

Ans. (A)


Can you elaborate how you reached the solution?

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Re: If A is the smallest positive integer that is divisible by all the int  [#permalink]

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New post 05 Sep 2018, 19:30
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GmatDaddy wrote:
If A is the smallest positive integer that is divisible by all the integers between 24 and 27, inclusive, and B is the smallest positive integer that is divisible by all the integers between 15 and 18, inclusive, the greatest positive number that divides both A and B completely is

A. 360
B. 720
C. 2160
D. 4320
E. 6480



So A is nothing but LCM of 24,25,26 and 27..
24=2^3*3
25=5^2
26=2*13
27=3^3
LCM =2^3*3^3*5^2*13

And B is the LCM of 15,16,17,18
15=3*5
16=2^4
17=17
18=2*3^2
B= 2^4*3^2*5*17

Now our answer is the HCF as we are looking for factor
A=2^3*3^3*5^2*13
B=2^4*3^2*5*17

Common factors = 2^3*3^2*5=8*9*5=360

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If A is the smallest positive integer that is divisible by all the int  [#permalink]

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New post 06 Sep 2018, 01:33
sidj20 wrote:
PKN wrote:
GmatDaddy wrote:
If A is the smallest positive integer that is divisible by all the integers between 24 and 27, inclusive, and B is the smallest positive integer that is divisible by all the integers between 15 and 18, inclusive, the greatest positive number that divides both A and B completely is

A. 360
B. 720
C. 2160
D. 4320
E. 6480


We have to find out, HCF(LCM(24,25,26,27),LCM(15,16,17,18))=HCF(70200,12240)=360

Ans. (A)


Can you elaborate how you reached the solution?

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Hi sidj20,

please refer the above post for detailed explanation.
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Regards,

PKN

Rise above the storm, you will find the sunshine

Re: If A is the smallest positive integer that is divisible by all the int &nbs [#permalink] 06 Sep 2018, 01:33
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