HCF

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Tue Feb 09, 2010 12:47 pm

Two numbers have 36 factors each and HCF of these two numbers is 36. What is the minimum possible LCM of these two numbers if the power of any prime factor in these two
numbers is not more than 3?

cube(2) Ã— cube(3) Ã— sqr(5) Ã— 7
sqr(2) Ã—sqr( 3) Ã— cube(5) Ã— cube(7)
cube(2) Ã—cube( 3) Ã— sqr(5) Ã—sqr( 7)
cube(2)Ã— 32 Ã— cube(5) Ã— sqr(7)
cube(2) Ã— sqr(3) Ã— sqr(5) Ã— sqr(7)

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Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 12:47 pm

Mom4MBA: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Fri Jan 22, 2010 1:10 pmFollowed by: 4 members; Location: New Jersey; Thanked: 13 times; GMAT Score:640

by Mom4MBA » Sat Feb 13, 2010 2:37 pm

The numbers with HCF 36 will be

2^3 x 3^2 x 7^2; number of factors (3+1)(2+1)(2+1)=36
2^2 x 3^3 x 5^2; number of factors (2+1)(3+1)(2+1)=36

Least LCM will be 2^3 x 3^3 x 5^2 x 7^2

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 18, 2010 6:00 am

Mom4MBA wrote:The numbers with HCF 36 will be

2^3 x 3^2 x 7^2; number of factors (3+1)(2+1)(2+1)=36
2^2 x 3^3 x 5^2; number of factors (2+1)(3+1)(2+1)=36

Least LCM will be 2^3 x 3^3 x 5^2 x 7^2

Hey Mom4MBA,
I guess you quickly picked the two no.s for the HCF.But suppose instead of 36 we had gotten some bigger no.(lets say 1036)
Is there a formal step-by-step approach to get to the number of factors and the corresponding HCF??

I find that this is one of my weak area I have been ignoring for quite some time.
Can you give me a good link for HCF and LCM related properties??

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Mom4MBA: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Fri Jan 22, 2010 1:10 pmFollowed by: 4 members; Location: New Jersey; Thanked: 13 times; GMAT Score:640

by Mom4MBA » Thu Feb 18, 2010 7:05 am

had this question been like:

Two numbers have 36 factors each and HCF of these two numbers is 1036. What is the minimum possible LCM of these two numbers if the power of any prime factor in these two numbers is not more than 3?

factors of 1036 = 2^2 x 7 x 37
let the two numbers be 1036 a and 1036 b
these two numbers cannot have any other new common prime factor otherwise HCF will change

Now we want each number to have 36 factors (3x3x2x2) or (4x3x3) other combinations will not be allowed as it will make the power of any prime number to go over 3.

(4x3x3) means these 2^3 x 7^2 x 37^2 ; 2^2 x 7^3 x 37^2 ; 2^2 x 7^2 x 37^3
(3x3x2x2) means one of the number can be 2^2 x 3^2 x 7 x 37 ; 2^2 x 5^2 x 7 x 37 [others will have larger values]

from the above numbers the lower two will give least LCM

So for minimum possible LCM a can be 3^2 and b can be 5^2

LCM will be 2^2 x 3^2 x 5^2 x 7 x 37

I don't know how to explain it in easier way, if anyone else can help...........

Stay focused

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pmFollowed by: 79 members; Location: New Jersey; Thanked: 109 times; GMAT Score:640

by money9111 » Thu Feb 18, 2010 7:14 am

Hey Mom4MBA,

where are you located in New Jersey? I'm from Jersey too!

My goal is to make MBA applicants take onus over their process.

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 18, 2010 7:41 am

Mom4MBA wrote:had this question been like:
Two numbers have 36 factors each and HCF of these two numbers is 1036. What is the minimum possible LCM of these two numbers if the power of any prime factor in these two numbers is not more than 3?
factors of 1036 = 2^2 x 7 x 37
let the two numbers be 1036 a and 1036 b
these two numbers cannot have any other new common prime factor otherwise HCF will change

Now we want each number to have 36 factors (3x3x2x2) or (4x3x3) other combinations will not be allowed as it will make the power of any prime number to go over 3.

(4x3x3) means these 2^3 x 7^2 x 37^2 ; 2^2 x 7^3 x 37^2 ; 2^2 x 7^2 x 37^3
(3x3x2x2) means one of the number can be 2^2 x 3^2 x 7 x 37 ; 2^2 x 5^2 x 7 x 37 [others will have larger values]

from the above numbers the lower two will give least LCM

So for minimum possible LCM a can be 3^2 and b can be 5^2

LCM will be 2^2 x 3^2 x 5^2 x 7 x 37

I don't know how to explain it in easier way, if anyone else can help...........

Hey Mom4MBA,
Thanks for the explanation u had given above.Its easily understandable and maybe in the most easiest way.
I guess the imp. properties we have to take note of are:-

these two numbers cannot have any other new common prime factor otherwise HCF will change

36 factors (3x3x2x2) or (4x3x3) other combinations will not be allowed as it will make the power of any prime number to go over 3.

from the above numbers the lower two will give least LCM

I thought that since 36 was a small no., you easily got to its factors.[For a small no.,we can easily use hit-and-trial]
But for large no.s hit-and-trial would have become very cumbersome.

Anyways,thanks again for the formal method.

Do you have any guide for learning the LCM and HCF properties??Any gud link would do.
On google search,I get wikipedia[https://en.wikipedia.org/wiki/Greatest_common_divisor]but lots of irrelevant information is also listed there and it gets kind of tiring going through the whole thing.
I need to brush up on the above properties so ur help would be appreciated.

It takes time and effort to explain, so if my comment helped you please press Thanks button

Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker

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Mom4MBA: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Fri Jan 22, 2010 1:10 pmFollowed by: 4 members; Location: New Jersey; Thanked: 13 times; GMAT Score:640

by Mom4MBA » Thu Feb 18, 2010 9:05 am

Good that you understood because I am no expert at explaining or finding a shorter approach. I just got started with my preparation. Actually I have few Career Launcher booklets and also Math book by HC Verma (not that good a book but some fundas are good), while coming to US what ever I could get hold of I packed. Sorry no good link that I know of.

Stay focused

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 18, 2010 9:23 am

Mom4MBA wrote:Good that you understood because I am no expert at explaining or finding a shorter approach. I just got started with my preparation. Actually I have few Career Launcher booklets and also Math book by HC Verma (not that good a book but some fundas are good), while coming to US what ever I could get hold of I packed. Sorry no good link that I know of.

Hey thats fine. You have written that you have CL booklets (Have u already given the MBA entrance exams??)
Also,HC Verma is a physics book,no??
I read it while prep 4 engg entrance exams.
Has he also authored any maths book???
So,I guess you are working in the US..

It takes time and effort to explain, so if my comment helped you please press Thanks button

Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Thu Feb 18, 2010 9:28 am

harsh.champ wrote:
Mom4MBA wrote:Good that you understood because I am no expert at explaining or finding a shorter approach. I just got started with my preparation. Actually I have few Career Launcher booklets and also Math book by HC Verma (not that good a book but some fundas are good), while coming to US what ever I could get hold of I packed. Sorry no good link that I know of.
Hey thats fine. You have written that you have CL booklets (Have u already given the MBA entrance exams??)
Also,HC Verma is a physics book,no??
I read it while prep 4 engg entrance exams.
Has he also authored any maths book???
So,I guess you are working in the US..

See Here..who is this?? they have started a" self proclaimed....happy pep talk among themselves...!!

A novel in the process??? Huh??

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Thu Feb 18, 2010 9:34 am

shashank.ism wrote:Two numbers have 36 factors each and HCF of these two numbers is 36. What is the minimum possible LCM of these two numbers if the power of any prime factor in these two
numbers is not more than 3?

cube(2) Ã— cube(3) Ã— sqr(5) Ã— 7
sqr(2) Ã—sqr( 3) Ã— cube(5) Ã— cube(7)
cube(2) Ã—cube( 3) Ã— sqr(5) Ã—sqr( 7)
cube(2)Ã— 32 Ã— cube(5) Ã— sqr(7)
cube(2) Ã— sqr(3) Ã— sqr(5) Ã— sqr(7)

Shashank,

Plz man..we beg u...y dont u post the questions properly?? Do u really feel people have that much patience in "deciphering" the codes u used??

Already we are here we want to get some knoweldge..But seeing all your posts..u never know man How many souls are"cursing" you for the trouble u cause..This is truth man..Plz dont take wrath of others( that too this way Buddy!)

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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Mom4MBA: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Fri Jan 22, 2010 1:10 pmFollowed by: 4 members; Location: New Jersey; Thanked: 13 times; GMAT Score:640

by Mom4MBA » Thu Feb 18, 2010 9:35 am

I am so sorry, that was RS Agarwal not HC Verma (ah, I still remember this book!)
My brother was preparing for CAT so I got few of his books, but the pattern and syllabus of CAT and GMAT are very different. I am not not working.

Stay focused

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